1.) Playback on the computer? It depends on the computer and the video editor you are planning to use. More detail, please.
Burned a DVD of the footage taken with this camera would it play on a standard American television set? North American televisions use 30 frames per second; PAL uses 25 fps. There are ways to convert, but none are "pretty". Where would the extra frames come from?

2.) The HDR-HC1 captures low-compression standard definition DV or high definition HDV format video to miniDV tape. With both a viewfinder and LCD panel, audio-in connection, manual audio gain control and a (shared) lens barrel ring that can be manual focus or manual zoom, it is closer to a "prosumer" than a consumer cam. Most high end consumer cams use flash memory or hard disc drive storage media that stores high compression AVCHD. The HC1 was the first of its kind - the HC3, HC5, HC7 and currently available HC9 followed. The HC1 has NightShot mode, Interval recording (for time lapse stills), a built-in flash, records stills to a Pro Duo flash memory cars, has a LANC port and a headphone port.

3.) Accessories: It came with a lens hood (Sony part 20596411) in the box. If it is gone, that can be replaced (from Sony) or you can use the lens hood made for the HVR-A1 (the HC1's "pro" sibling - Sony part 263297101). Since the HC1 has a 1/8" (3.5mm) stereo audio-in port, an XLR adapter (BeachTek, juicedLink among others) can be used - so basically any mic can me used. I use a NRG Research "shotgun" mic, Sennheiser wireless lavalieres and Shure handheld wired mics.

4.) I got mine in 2005. It has been a workhorse (along with my HDR-FX1. It has an odd LCD panel issue at the moment, but I am able to work around it.

As a miniDV tape camcorder, your computer needs a firewire port. Your video editor needs to be able to deal with HDV format video, too.