Ive used some of Georgia Tech's most powerful telescopesWe have telescopes, satellites and data from spacecraft. You can buy a telescope yourself from a department or electronic store. There are also observatories that the public can visit. Telescopes at observatories are very powerful. Many celestial bodies can be viewed with the naked eye. You can view our neighboring galaxy, Andromeda, without a telescope.
No, they cannot prove that "planets" exist up in the sky