For the first problem, it might be something as simple as how your list is sorted. From inside iTunes you can click on the different columns (Song name, artist, album, etc.) to sort whatever list you're in by that criteria. Do you perhaps have the list sorted by play count? Or more specifically, by reverse play count (same thing, but it reverses the order)? That could explain songs dropping to the bottom of the list after you play them. Everything's at zero plays, so it sorts by some secondary criteria like Track Number, but then once you play one it jumps to the bottom of the list because it has more plays. Try sorting your list by something else like Artist or Date Added. Or, my favorite, click the "Album" heading to sort by album name. Click it again and you'll see it change to "Album by Artist." Once more and that changes to "Album by Artist/Year." That will sort it like so:
Artists sorted alphabetically (AC/DC before The Beatles before Cream, etc.)
Within each artist, songs are sorted into albums, either by release date if you've entered it or else just alphabetically.
Within each album, songs are sorted by track number.
Your second problem sounds like it might be a tagging issue. This can happen if you import songs from different sources. Say for example you imported a CD into iTunes, but there was a scratch so one of the songs didn't import correctly, so you download that song from iTunes. The info for the downloaded song might not match exactly that of the imported CD. Or it could just be due to importing badly-tagged songs from other sources.
Make sure that the songs on an album's tags match each other exactly
for the Artist, Album Artist, and Album fields. Capitalization doesn't matter (at least, I don't think it does), but spelling does, and any leading or trailing spaces, or double spaces between words will cause it to read as a different tag. The best way to make sure that they all match is to batch-edit them: select all the tracks at once by shift-clicking a range of tracks or ctrl-click to select individual ones, then right-click any one of them and select "Get Info." Any field with a value in it, is shared by all of the selected tracks. Anything that's blank is either blank in all tracks, or has a different value for one or more tracks than it has for others. Enter the correct information, or just check the box next to any blank lines you'd like to make sure are clear, and then hit "OK." Then make sure the list you're looking at is sorted by something sensible like Album, and see if they sort right.
If that didn't fix it, it might have something to do with the sort fields. The sort field is how iTunes knows to sort The Kinks under "K" for "Kinks" instead of "T" for "The." Simple stuff like "A" and "The" will be handled automatically by iTunes, but you can also manually edit them as well. Select all songs on the offending album and make sure they either all have the same
sorting info for Artist, Album Artist, and Album, or else nothing at all in those fields (check the box next to an empty line to make sure it's actually cleared, rather than has a different value for different songs).
take care of your problems. If it doesn't, feel free to post back here and we'll try to "sort it out" for you