a) There's an import duty for flatscreesn: 10 % duty (I think) plus 13 % VAT
There is also a restriction on how many DVDs you may bring, I think it is 200. Check with your shipping co.

b) For analogue TV, China uses PAL whereas the US standard is NTSC. As long as your TV supports PAL, you'll be fine.

c) If you're happy with a TLC - TV it will set you back 2,000 CNY and up, depending on size, of course. See, for example, www.suning.com

d) Most apartments in China are furnished; i.e. there are at least two or three TVs.