That model is limited to 1920x1200, via a single link DVI connection. Only the MacBook Pro systems from that era had a full dual link DVI connector, prior to Apple switching over to displayport.

To get video out, you will need to track down an adaptor to go from the weird mini-dvi port to standard DVI or VGA.

No real suggestions on a KVM, but as long as it supports USB keyboard and mice, along with DVI for video, you should be good. Just keep in mind the dual link DVI requirement on your monitor (if using DVI) also applies to the KVM if you want to retain your 2560x1600 resolution from your main PC.