what happened to the god old days of plug an play routers, autodetected everything... "Sigh" anyway the wireless thing what type of wireless connection is it? b? G? or even the rare and obscure A?
anywho almost all wireless products generally do that sometimes, they peak, they fall, they disconnect, and then they spike up again. this is due to the fact that wireless doesnt have a steady contact with the comp. it sends signals tthrough airwaves instead of wires= less reliable.
For your second problem, make sure you have all the info from your ISP.
Ip adress, Dns, Default gateway, etc.. you should have gone to the router thing and configured your router to those settings correct?
if you havent do that immediatley that could be the cause. usually to connect your router to enter setting try typing 192,168.1.1 in your IE or Firefox Bar that should take you to your router. and as for the tv thing I havent a clue. hopefully that helps. and if you want a more stable wireless, try going with wireless G, and or getting a better antenna for your wireless router to boost the signal. or screw wireless completeley and go buy yourself some hundredfoot Cat5's