Yep, anything under 2000 KB is suspicious & should be disregarded (any song under that size would be either really short or at such a low bitrate that the quality would be really awful).
* WARNING: Viruses on network you should be aware of ! * Virus thread: Typical virus spam file sizes - Make a note of them (click on blue link to see) Fake files showing up in search results
The 'your name's LimeWire Tunes' in iTunes is just a playlist. All a playlist does is tell your computer where to find the music files - there aren't any actual music files in that list. So you can't create playlists or move songs to an iPod from there.
How to transfer music to my iPod (& iTunes)
If you delete files from the iTunes library then they won't play in iTunes any more. The ! symbol means that the file isn't in the iTunes library.
If you have problems with search results appearing slowly, you can also vary your search terms a bit. Look for artist or album, rather than song title. And try the 'All Types' search... sometimes that can yield different results.
Also see:
How to find music(tips for movies, too)