Adobe maintains that the formats that go into Premiere Elements are those which come out of a camera. FLV does not and so it is not supported. I remember seeing this as an official response to a similar question (Can't find that thread)
To answer your questions to the best of my knowledge:
1. Do not change the output frame rate to 25 from an external software. I say this because there are many algorithms that convert a 30 fps to 25 (Which frames are dropped, what happens to P-frames, bidirectional frames etc.). And Adobe will best understand an algorithm that is theirs. So keep the frame rate to 29.97 when converting to DV-AVI
2. Convert the video to a project setting that Premiere Elements has. You want a Widescreen, so do a 16:9, 720x480, DV-AVI. This video when brought into Premiere Elements will switch the project automatically to the NTSC DV Widescreen
3. I don't know this. There are too many things that could have gone wrong. The downloader could have encoded differently, the original file would have been this resolution but youtube chose to "categorize" this as 480P since it is the closest preset for them. VLC could be showing it wrong. Cconvert it to DV-AVI and you will surely see some borders but should not really be an issue once viewed in Full screen. I personally stop noticing them after a while and it is not a pain, for me.
4. Use DV-AVI. Premiere Elements simply likes it