the sun - If we were to see the Sun with our naked eyes from the Orion belt, would all planets be encompassed inside the star? Is this calculable?

Such observations are possible, see Fomalhaut b.
It depends mainly on the diameter of the objective of the telescope (diffraction limit) and contrast. Telescopes can (at least in theory) be combined to an effective telescope of larger diameter (aperture) by interferomentry.
Masks can help to occult bright stars to overcome the contrast limitatios.

There are indirect methods to "see" faint planets, as e.g. applied in the Kepler mission, or by Gaia.

And yes, it is calculable. With naked eye we wouldn't be able to distinguish the sun from the planet orbits from a distance of about 1000 lightyears, as the orion belt stars: 1000 lightyears are about 300 parsec. This means, that the earth orbit would be about 1/300 arc second. The resolution of the human eye is about 4 arc minutes, the 72,000-fold. For Pluto it's still more than 1000-fold.