Since I have installed a router, I cannot transfer files >~1 KB anymore. Does anybody know whats the problem?
Short answer: Ugly problem, there is no fix, but a workaround exists everbody uses. If you have a real router pester your vendor (or RTFM), if it is a linux box, make it use mss clamping.
Do I have to set free any ports on the router?
No. Your problem probably is your MSS/MTU.
Let's speculate: you use DSL. You have an internal network, and some kind of Linux Box or soho router inbetween.
Problem here is: on your Ethernet (and also on most IP Backbnones) the MTU size is 1500, which in turn means an MSS of 1460. Now, in order to squeeze a PPP header between the ethernet and the IP headers, your PPPoE stack only has a MTU of 1492, which translates into an MSS of 1452.
Now all this should work magically - though a little inefficient - with IP without you noticing any trouble. Old implementations would just fragment the ip packets down to 576 bytes, while more recent implementations (like, 8 years or younger) try to determine the actual path MTU and use that one instead. But to do this they haver to rely on the routers inbetween to be standards conformant ... and neither Deutsche Telekom nor quite a few other DSL vendors feel any urgent need to conform to well established standards (like Internet RFCs) - they think pissing of customers with routers is ok, and who needs standards anyway ?
Since SOHO router vendors know this, most SOHO routers have a hack built in which messes with TCP connection setup to force windows to use MSS 1452 anyway. Linux and BSDs can do that as well - on Linux they call it MSS clamping.
Get your router to limit the TCP MSS to 1452, and you should be fine.