1.) No, component is higher quality connction method. If you have a high quality TV and a progressive scan DVD, you'll see the difference with the component connection.
2.) If you will use the HDTV, it's better to buy one with the built-in convertor. Many are HDTV ready, but require an externa decoder similar to those old cable boxes from the 80's and 90's. Figure on an extra $500 to $1200 bucks for one of those.
3.) Widescreens are nice if you watch alot of movies. Even though it's a 16:9 you will NOT get rid of all the black bars on the top, though they will be far less noticable. Most movies on DVD today are displayed in anamorphic (2.35:1) ratio, which is 21.15:9 (on a 16:9) or 7.05:3 on a (4:3). Also, future regs will be replacing 4:3 broadcasts with full 16:9 broadcasts in the US. It was supposed to be done by now, but has been pushed back. Might as well get a 16:9 one now if you're planning on keeping this for awhile.
STAY AWAY FROM PLASMA! They're still considered "new" technology. You'll pay way too much, and get no real gain (at least noticable). Not to mention they have a short lifespan, not to exceed between 5-10 years depending on a bunch of things.
The best projection-type (big screen) TVs are made by Mitsubishi, Toshiba, and Hitachi. The best standard (under 36") are by Mitsubishi and Sony.
Mitsubishi far excels everyone in this catagory in the large screens, as does Sony in the small screensand. The prices are good for what you get (quality). HH Gregg (Best Buy, Circuit City type of store) has a Platinum Series 55" 16:9 Mits for $2099 this past week, well worth it. They also have a gold series, which is older and doesn't have the built in HDTV decoded. It's worth the extra $400 to $500 for the platinum.
On a side note, stay away from Zenith. They are junk...even though your parents or grandparents had one that laster forever, the company isn't the same. In the 90's they finally folded, and someone else bought the name rights...now placing cheaply made junk into stores with a Zenith logo.