I know very little about Star Wars, but I'm curious how powerful the Force truly is.
Yes. There is at least one example of a Force-user prolonging their life by thousands of years using the Force. It is also theorised, by Winter and Luke Skywalker, that Jedi would be capable of using the Force to slow the ageing process in Dark Force Rising. Palpatine, Yoda, and C'Baoth were the object of their discussion; C'Baoth was well over 100 years old by that point, despite being human (as it turned out, the C'Baoth in question was a clone, so the discussion was moot).
There are also other beings who achieved extremely long life-spans through the use of the Force, though this may have been a natural part of their existence, rather than through any Force-related assistance. There were multiple attempts, mostly by Dark-Siders, to achieve immortality through the Force.
In Disney canon, Darth Sidious plotted to use the power of the dark side to rule for ten thousand years:
Such perilous machinations required two Sith, one to serve as bait for the dark side, the other to be the vessel. Success would grant them the power to harness the full powers of the dark side, and allow them to rule for ten thousand years.
Biotechnology in Star Wars has not yet advanced to the point at which humans can live for ten millenia, so I think we can safely say that Sidious was planning to use the dark side to attain immortality, as well as ultimate power.
There was a Sith Lord that couldn't be killed, Darth Sion, during the Old Republic (around 2800 BBY). He ressurected multiple times and surpised and killed a lot of jedi. His power was gained through meditation and chaneling his hate towards the jedi. The darkside consumed him, tuning him into a corpse (held together by the dark side of the Force), and caused him constant huge pain, used to fuel his power. In the end he decided to give up his hate and allowed some jedi to kill him. It's somehow similar to the way in which Darth Maul survived the first duel with Obi Wan, by focusing his hate. So, yeah, sith could potentially live forever only by deeply hating Jedi Order.