Any of the dual-headed Radeon 2400-2600 cards should work fine. Size the OS with what you want the machine to do, a sever is what it is, not a gaming machine.
Any PCI-E graphics card will work.
You should not remove any component from your graphics card setup.
You will probably need a dedicated graphics card to play any newer games.
There's a special breed of cards out there that aren't afflicted by the fans whirring noise called passively cooled cards.
There are hundreds if not thousands of reviews of different types of graphics cards available online, viewing several of these is a good way to find out the basics and information on what graphics cards are most often recommended for specific purposes. A local computer technician or knowledgeable salesperson would also be able to provide information on graphics cards and answer any specific questions.
Any integrated graphics chip draws upon the system RAM. Only discrete graphics, or graphics cards, have their separate RAM supply.
There is a high probability for any monitor to work with any graphic card.
There's no significant difference -- all graphics processors will produce a varying amount of heat depending on the workload.
Sure you don't mean "which Apple is best for graphics"? Not to sound like a PC fanboy, but Apple is extremely limited in their support of higher end or any graphics cards. Most of the cards that run on their machines are made to run on specifically those machines; with a PC, there are quite literally thousands of choices depending on the vintage of your computer. Put simply: Apple is not best for graphics, and if you are asking "which" is best: anything that's way too expensive for the average Joe to afford.
According to the internetgames.com website, they have Nvidia GeForce GTX 570 listed as the number one graphics card. They also list another 14 excellent graphics cards any gamer would be happy to play on.
any pci or pci-e video card. such as ATI Radeon video cards (not agp ones) or NVidia GeForce video cards (again, excluding the agp ones)
No, you need a pci express or pci express 2.0 graphics card to play this game well. Then again, it depends on what YOU would consider "well".