OK, I'll have a go although you really shouldn't combine so many questions into one.
1 The mutation protection "paradox"
As already mentioned while many mutations are caught and corrected, not all of them are. You have to consider that a body (the human one, for example) contains several trillion cells, each of which contains 3 billion nucleotides each of which can be mutated. So, if the human body has, say, 50 trillion cells (a relatively conservative estimate), that means that a mutation could occur at any of
$3e10^9 * 5e10^{13} = 15e10^{22}$ = 150000000000000000000000
different sites. So even though the cell is pretty good at catching and correcting errors, some are bound to get through from pure statistical chance. In any case, you know that not all errors are corrected, diseases such as cancer are often the direct result of such mutations and errors.
I should also point out that in sexually reproducing species (such as humans) mutations are passed on to offspring only if they occur in one of the cells that become gametes (sperm or eggs) so this does not accurately represent the number of available sites that can give rise to mutations that can directly affect evolution for sexual species. Other species however, do not reproduce sexually. For example, cutting a worm like C. elegans in half will result in two worms so a mutation in any of its cells could be passed on to its offspring.
Anyway, point mutations are not the only way that diversity is generated. Even in the absence of mutations, processes such as chromosomal cross-over during gamete cell division (this is what makes you into a mixture of your Mom and Dad) would still produce differences that selection can act upon.
2 Genetic entropy
This one is a bit harder to answer, largely because it is complete poppycock. I'll try though. Let's see, we do not have "more mutations than our parents", what an absurd idea! The silent assumption here is that there was a "perfect" genome and each mutation is carrying us further from it. Therefore, since my parents were closer to this platonic ideal of the perfect DNA, each mutation that occurs in my cells takes their genomes a further step from that perfection.
This is very simply wrong. There was never a perfect genome, each cell in each individual of each species in the world is constantly undergoing mutations and has always done so. The genome is dynamic, not static and it has never been static, it can't be. DNA is a chemical substance and undergoes chemical reactions (such as mutations) all the time. Like all other chemicals it exists in a thermodynamic equilibrium, but not a static one. The only way that I have "more mutations" than my parents is if you accept as a premise that humanity comes from the perfect genomes of Adam and Eve. Since this is what Mr. Sanford is, presumably, attempting to demonstrate, using it as a premise is, at best, a circular argument.
Unless you assume the existence of a platonic ideal of a genome you cannot say whether I have more or fewer mutations than my parents because how can you compare them? In order to say that I have more mutations than my parents, you would need to quantify the number of mutations that each of us has and that cannot be done. How do you count mutations? You would need a reference genome of the ancestral human and we don't have that.
The rest of the argument is even more nonsensical. Mutations can either be completely neutral and therefore "unselectable" or they can have an effect. By definition, if a mutation has an effect, it can be selected for or against. That's how selection works. So, stating that these tiny mutations (which do exist) cannot be selected for/against and yet are harmful is a direct contradiction. You can only have one or the other. If they are harmful, there will be a selective pressure to change/correct/lose these mutations.
In any case, if these things "are left to build up in all people until the entire human race becomes extinct" all that means is that these things build up in individuals of a species and the species changes. Ummm, well, yes, we have a name for that, it's called evolution.
Just a final point, tRNAs have their own specific genes, a random mutation in an intergenic region will have no effect on them, why should it? This just shows the fundamental ignorance of the author in question.
Oh, and the whole "Junk DNA" is a very complex question. Yes, we now know that a lot of what was termed "Junk DNA" has a function (this was no surprise by the way, "Junk" was never intended to be taken literally). All this means is that mutations in non-coding DNA can also be harmful. OK, fine, then they will be selected against because that is how evolution works.
3 "meta-informaton paradox" (whatever that is)
This idea is often bandied by creationists but is a basic misunderstanding. Mutations are random(ish), evolution is not remotely random. Advantageous mutations that make an individual more likely to reproduce will tend to be selected for and spread across a population while deleterious mutations will tend to be selected against and be removed from the gene pool. This is not a random process at all.
As for the "meta-information", nothing is "independent". The cell is a complex system with extremely complicated interactions and a lot of cross-talk between the different processes. The DNA is not separate from the cell, it is an integral part of it. The Aristotelian idea of reductionist logic where you study complex systems by cutting them into little bits and understanding those bits is all very well as an intellectual tool but that is all it is, a tool. In reality, complex systems should be studied in their entirety, you cannot disassociate DNA from DNA regulation.
4 The pseudo math hypothesis
Let's have a look at these assumptions.
Assumption 1: "Evolution must occur by a net gain in new information. "
Of course not. Evolution can create a net loss in complexity (information) just as often (indeed, probably more so) as a net gain. The classic example of this are viruses. They have evolved into lean, mean, minimalist killing machines. They have nothing that is not absolutely essential. Hardly a net gain in information.
Assumption 2: I don't know where these numbers are coming from, whenever you read a phrase that starts with "scientists have observed", run away. What scientists? How have they observed this? How do they define beneficial? Anyway, let's say these numbers are right (I really really doubt it, but let's say they are for the sake of argument).
Assumption 3: Huh? Let's just throw some random numbers and see if they stick. There is no magical number of changes that results in speciation. In mutations as in real estate, it's "location, location, location". The question is not how many mutations but where they have occurred and what effect they have had.
Assumption 4: Wow, this one is just completely wrong. To pick just one problem here, if 10 million species is the upper limit of species living today, and 99% of all species have become extinct, how does it follow that 10 million can also be a good estimate of all the species that have come before? If the 10 million of today are only 1% of all the species that have ever lived (99% are extinct right?) then it follows that the number of species that have existed is around one billion.
Assumption 5: It is most certainly not true that every beneficial mutation is fixed. Many are, others aren't. Also, bear in mind that the same mutation can be both beneficial and harmful in different contexts. For example, a mutation that makes me more resistant to cold would be very useful during an ice age but less so (and could be harmful) during a period of high temperatures. To take a classic example, there is a known mutation in some humans that makes them susceptible to sickle-cell anaemia. However, the same mutation also protects from malaria. So, is this one harmful or beneficial? That depends on whether you are living somewhere where malaria is prevalent or not.
OK, so now the numbers. These wonderful probabilities all assume that evolution happens through "beneficial" mutations. First of all, that is not the only way that genomes change. I mentioned chromosomal crossing over earlier and you also have things like genetic drift (you also have all sorts of other weird things such as horizontal transfer).
In any case, it does not take X beneficial mutations to make a new species. As I said, there is no magic number and evolution is not restricted to beneficial mutations. Just mutations.
However, the most serious problem in this reasoning is that you are not calculating probabilities, you are calculating frequencies. What the argument you are presenting says is that it will take $10^{150billion}$ events for 10 million species to evolve from a common ancestor. It says absolutely nothing about the probability of such events because you are not taking into account the size of the event pool.
Let me explain, if you toss a coin, you have a 50-50 chance of getting either heads or tails. Therefore, getting 5 heads in a row is not very likely if you throw five times. If, however, you throw a few billion coins a few trillion times, you are very very likely to at some point get 5 heads in a row. In order to calculate the probability of something you need to take into account the number of tests performed.
If we keep the arbitrary numbers you have quoted, we have 10 million species, let's say each of them has a genome of 1 million base pairs and each has just 10 cells whose genome is passed on to their offspring (non-sexually reproducing species are actually the vast majority but most of them are unicellular so let's just take 10 as an average). Let us also assume that the creationists are right, the world is about ten thousand years old and let's say that species live for an average of two years (absolutely wrong of course but let's just pick small numbers). Finally, let's say that each species has only 1 million living individuals (again wildly conservative, just think of the number of ants in the world). This means that we are talking about
10 million species * 10 cells each * 1 million individuals * 1 million bases per cell = 100000000000000000000
If the rate of mutations is a tiny (much much smaller than the real value) 1 mutation every 24 hours, this means that there are $10^{20} * 365$ potential mutations a year. And, therefore, there have been $10^{20} * 3650000 = 365*10^{23}$ opportunities for mutation in the last 10000 years, that's 365 followed by 23 zeroes, that's a hell of a lot of chances. So, yes, if one in a thousand of them were beneficial that still makes it really quite likely that such mutations have occurred and have caused speciation events. This becomes even more likely if we take a realistic estimate of the time elapsed (10000 years is extreme for all but the most bullheaded of creationists).