Mostly planets transiting their stars are deduced through periodic slight dimming or the wobble of the star that is deduced as a planet’s gravitational pull in orbit.
I think the resolution from something 100K miles away and 100 light years would differ.
Wobble (or Doppler) and transit methods are the most used methods, yes, in that order. Resolution beyond a single pixel using direct observation is of course not possible without an objective lens the size of the whole solar system or something. But even a single pixel can reveal a lot, such as chemical composition using spectrography. We’ll see what the James Webb can do over the next few years.