Part 1 is pretty easy - just use an Advanced Search on the FIDE site and it will give you the answer. The lowest rated GM at the moment is Nicola Spiridonov from Bulgaria with a FIDE rating of 2135. He also happens to be at least 77 years old.
Unfortunately, I don't think the Advanced Search function returns a player's peak rating, just their current rating, so I don't know how you'd go about answering your second question.
Grandmaster is a lifetime title.
Who's the grandmaster with lowest Elo rating?
Who's the grandmaster with biggest loss from peak rating to the present rating?