If I connect it to internet in sweden, will there be any problems with online updating\gaming? (for example will I be able to play other swedes)
No problems. The only gotcha is to find out which region your Wii is supposed to be from and set it for that region as some downloads arent available in certain areas. For example someone had a USA Wii in asia and when he selected his country he couldnt download the browser. I told him to set the Wii to USA and it worked
Can I play PAL-games on the wii (no clue what chip I have)
Well yes and no. Is your Wii NTSC and is your TV NTSC? Most games note which video standard they are and even PAL games can be patched to run on NTSC systems.
Can I see what kind of chip I have? I thought it would be more like my modded xbox with new software and such
Impossible unless you take the Wii apart and connect the chip to a programmer. The Wii modchips are completely invisible to the system. In fact the "DVD upgradable" chips are especially amazing and dangerous if you understand how they are working.
I didnt even know that it had an online feature, does it cost money to use?
No unless you want to spend money buying games through the internet from Nintendo.