What are the benefits of running a bitcoin daemon? Can I get some fees on others transactions coming through my PC (creating blocks or whatever)? Transit-fees I mean.

Can I get some tiny bits of newly mined BTCs just on keep running bitcoind.exe in the background in 2013 and later?

Any other profits of keeping the full bitcoin database instead of using lite thin clients like MultiBit?

The bad side of MultiBit is you can not set the full zero fee. Official bitcoin wallet does.
You will not get anything money wise from running bitcoind, however the Bitcoin network depends on people running it for verifications.  Its providing a service to the rest of the bitcoin community.  I run it because I participate in the bitcoin community and want to give something back.  

This is how the "decentralized" part of the bitcoin protocol works.  People like you and I run the daemon and it verifies everyone elses transactions, the more people who run bitcoind the more secure the network becomes.

As for your other questions, I can't speak to speculation and this website will suspend your posts if you ask opinion or theoritical questions.