Hello and welcome to the forum!
1) I always read about getting graphic cards, would actual server hardware do a good job too? E.G i would try mining with a 1Gbit connected rootserver with Xeon i7 W3520 4x2(HT)x2.66+ GHz and 24 GB Ram
CPU mining is not cost effective - GPUs are vastly more powerful and have therefore set the standard for mining. No matter which CPU your server has, it would cost more on electricity than you could gain in bitcoins. Even if you don't have to pay for the energy, bitcoin-income would be abysmal.
2) What if i need to reinstall at some Point, do i have to spend the bitcoins and just download a new client afterwards? Or would it be a good idea to have one "save" banking account for generated coins? At some point every computer will crash i think...
The coins are "inside" the wallet.dat file - you should back this one up before you reinstall and on a regular basis to avoid and coin-losses from computer crashes. You should probably think about encrypting it before you back it up.
Alternatively there are online wallet services like mybitcoin.com which save you the hassle of dealing with your wallet.dat. You have to trust them however to keep your coins save.
3) Even if I'm connected with 1Gbit to the Internet i have 1 or max 2 connections, mostly 0 how comes that? Do I need to wait or what I'm doing wrong? Should I use a differnt client for mining then the official?
You probably have to wait a bit before you get more connections. The connection speed is not very important for the operation of your client. If you plan on mining, you should use some of the specialized GPU mining programs out there instead of the official client.