If we had the right technology could we see a distant star in detail? If, for instance, Hubble's camera was a $10^{300}$ times better, could it see a distant star in details, or is there a limit to the amount of light that reaches the Earth's orbit or perhaps does the light get distorted on its way so you must come closer?
Is there a limit to the number of light beams that hit a telescope camera's &quot;eye&quot; or if you built a huge telescope would you then be able to see that distant star in high detail (for instance, see an earth size satellite around Betelgeuse's orbit).
The only limitations would be related to building an instrument large enough.

There's a limit to the size of the finest detail a telescope can see. "Size" here is angular size, the angle that the detail is covering in the visual field. For a given wavelength of light, the smallest angular size depends on the aperture (diameter) of the telescope in a linear fashion: double the aperture, and you cut the angular size in half.

Rule of thumb: 100 mm aperture has a resolving power of 1 arcsecond, for visible light (not exactly, close enough). Therefore 200 mm aperture has 0.5 arcsec resolving power, etc.

By building larger and larger telescopes, the angular size of the smallest details becomes smaller and smaller. But are there any limits here?

There aren't any cosmologic mechanisms that I'm aware of that would prevent telescopes from operating at arbitrarily large resolving powers (arbitrarily small angular sizes). But we can't build arbitrarily large instruments.

The biggest monolithic (single mirror) telescope has an aperture of 8.4 meters. Using segmented mirrors, the aperture aim of the current largest project is 30 meters - the Thirty Meter Telescope, still in a very early stage, completion date unknown.

Beyond that size, large scale interferometers are the only option, with synthetic aperture varying from dozens of meters to kilometers, and larger projects are being discussed.

In theory, very large scale interferometers could be built in space. But there might be inherent limits for the aperture of such systems. Anyway, this is hypothetical.

EDIT: Giant telescopes in general do not require a continuous surface of glass. Interferometers almost by definition do not use a single reflector. You could build a gigantic telescope or interferometer where the active reflective surfaces are just these tiny chunks at the periphery of a huge perimeter. Most of the area in between is empty / unused.

EDIT2: The performance of the "tiny chunks" reflector is not the same as the performance of the full size mirror, as mentioned in the comments.