1) Is it advisable to go (partially) open source?
It's not really as impactful a decision as you think. Primarily, it would be a marketing move to attract a GNU/Linux audience. For games, being open is not particularly useful to the main audience of your games.
or will you get (lots of) clones then?
IMO, cloning, as Rubicon states, is based on success. Your source being open is irrelevant. Does it make it easier to clone? Probably. But, if your game is a success, the "challengers" likely have the resources to copy pretty easily.
How far will a GNU license really protect your software and code?
Only so far as you are willing to enforce it. This is not as glib as you think; it costs some serious dough to defend a license dispute. OTOH, lots of free legal help can be had for GNU-type stuff...
2) Should it be cross-platform? Because some people told me linux fans are usually more into indie stuff...
The GNU/Linux gaming community is very, very small relative to the Windows one, and has a heavy "techie" aspect to it, meaning either hardcore gamer or doesn't have time for any games.
3) Is the performance very important if you want to run the logic on a server? I mean cost-efficiency 'n stuff... What part of the LOGIC (ie not rendering / doing the 3D stuffies) would be the heaviest (maybe tcp? maybe pathfinding?) assuming I'm not going to get a pc-shredding AI.
I'm not sure what you are asking here. I guess you are talking of a multiplayer or MMO type game? If so, due to scaling, performance of any subsystem is important.
4) Are there any other things that I should be very aware of when making decisions of this sort?
Yes, danger lurks around every corner... :ninja: