A really impressive number of discoveries have been made since 2001 -- there's been kind of a proliferation of new sub-fields, so it seems like there's never any shortage of things for newcomers to work on.

There are definitely areas that haven't really been explored fully yet, like the use of SAT solvers in new and inventive ways to tackle difficult Life problems that are currently just beyond our reach.

Just for example, there's the problem of finding a fast elbow for a 2c/3 "signal wire" --

  https://conwaylife.com/wiki/Wire#2c/3_wire

It's not clear if SAT solvers can be applied usefully to glider synthesis questions, like "is it possible to collide gliders to build a Sir Robin spaceship?" At the moment that particular question seems way beyond reach, but maybe in a few years we'll be running an AI that is experimentally setting up new SAT solver problems, and something will pop up that we just haven't managed to think of yet.

Question 2: Wikipedia's articles tend to be very good quality -- partly because if they weren't, there are a lot of Lifenthusiasts with some experience maintaining the LifeWiki who would immediately go and fix any technical errors that might show up on Wikipedia. But the really detailed documentation on Life is definitely kept in the LifeWiki, not on Wikipedia:

  https://conwaylife.com/wiki/