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You will need a miniDVI to VGA connector (this is for the computer, the tv does not need an adapter), and a VGA cable. It'll cost around 30 for both things.
Typically the worst case scenario if your Windows partition got a nasty virus is that you'd only lose your Windows data. The Mac side would remain unaffected.

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Viruses that bridge between operating systems are extremely rare, and I haven't heard of any on the Mac side of things (there was a Windows to Linux one in 2002).
Most viruses now are not destructive, as hackers want your computer to continue to function as SPAM robots and the like, and breaking your hardware is rarely a good business model when they could control it instead. And if they control your Windows side... they wouldn't have any control of your Mac side.

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I have managed several Macs running Windows, in Boot Camp dual boot setups and virtualization (Parallels) setups, and no one has ever had any problem on a Windows partition that reached over to the Mac partition (nor any virus whatsoever that wasn't picked up by Symantec Antivirus Corporate). While it is theoretically possible, I would just put on some anti-virus software (links to free software below), and to be on the safe side back up your important data to an external Mac formatted hard drive.
No, a virus wouldn't affect the MacOSX... There are actually no problems that i can think of as long as you install windows the correct way with bootcamp.

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I've tried using HD cables and failed miserably. The easiest option here is to make sure your tv has a VGA connection. Its probably labeled computer connect. (its a small trapezoidal shape with two screw points next to it.)
(the cable that came with the mac mini [miniDVI to DVI] is mainly for monitors.
However, if a particularly nasty virus got hold of the Windows side that actually affected the hardware in a large scale, such as causing the machine to catastrophically overheat or wipe out entire hard drives, the Mac side could be affected then.