I doubt it, 1280x1024 monitors were the standard for LCD back then while CRT monitors already accepted higher resolutions. Lower than 1024x768 is last century.
Back in 2004, LCD monitors weren't all that common though. For a proper 2004 gaming card such as GeForce 6600 GT, 1024x768 was a common resolution (which you can verify by looking up some reviews for it), and from reviews from 2004, you can fairly easily find even lower resolutions. 1024x768 wasn't great even back then, but it was definitely not bad either, and lower resolutions appear to have still been fairly common. For high-end gaming, obviously lower resolutions must have been extremely rare, but a lot of gamers were probably gaming on cards worse than GF 6600 GT back then.
Yes, it was. The first HD game was shown in 1993. HD sets were released to the consumer in 1998. My PC monitor was 1280x1024 in 2003. PS2 and Xbox could output 720P and Xbox up to 1080i. Laptop screens of that time period were typically 1280X800 on a 15" Laptop.
Uh, when I said 720p, I meant exactly 720p and not 'something close but actually different'. From what I can remember, widescreen was just starting to get actually popular in 2004. Exactly 720p wasn't really a widespread gaming resolution in 2004 as far as I know, and a quick search for graphics card reviews from around 2004 supports this view.