Unlimited time and servers

I wonder if ongoing unlimited time games are able to make weight to the servers. case in point, for example sometimes in an unlimited time game, loser doesn't resign and just closes the page. So because of game has unlimited time, this game never ends. I have two ongoing games because of that and one of them is older than three months lol. So i have three questions here,

1. are these ongoing trash games make an effect on lichess servers?
2. can there be any automatic end process for these games if for example a player doesn't make a move after, i don't know, a week? Because i am pretty sure i made some mistakes and inaccuracies and want to see comp. analysis. Because of that (the game hasn't ended) can't make a comp. analysis.

3. Can we at least make an automatic ending process for the games against "anonymous" players?

for example http://tr.lichess.org/uxRMOZP9FUyR
obviously i won here as white but i honestly think my opponent had decent chances in some certain positions during game and want to see it analyzed.

I see your point, but unfortunately "unlimited" means unlimited. Lichess has no right to end games arbitrarily.

Don't worry about the server: idle games use no more resources than finished games.

Under profile, we have tabs called: Games Played, Rated, Wins, Losses, Draws and Bookmarks.
Maybe add another tab call: Unfinished Games (Games in progress).
It might help people remember that they have a game running since last month. People that do correspondence chess would most likely like that feature.

The tab exists. It only appears when there are some unfinished games to show.