ITunes authorization and song selection/playback issues

Question

I use my computer (macbook air) and iTunes for work (I am an itinerant elem. music teacher).  The computer does not have a disc drive, so I import music from CDs and use iTunes match to transfer tracks to my laptop or iPod. 
I'm having a few issues with iTunes (11.0.5) that have been occuring recently.
1) I play a song from a playlist with no issues, then play the same song later (sometimes just minutes later) and receive a prompt saying I am not authorized on this computer to play that song and that song only.  Entering my ID and password gets rid of the prompt, but causes iTunes to freeze (I usually force quit and restart the program, which sometimes fixes the problem and sometimes doesn't).  I use iTunes match on this computer, but it still allows me to play other songs from the cloud while one song has authorization issues.
2) When searching for a song using the iTunes search bar I used to be able to double click on the matching items without pressing enter (as I type in the search query it brings up options, which I can then double-click to play without completing the search).  Lately, when double-clicking on those songs they either don't play at all, or an entirely different piece of music will play.  If I click again it will cycle to another (also wrong) piece of music.  Despite what I type in the search, the songs that play when I click are songs with trumpet in the title somewhere, with the exception of one song, which is a trumpet sonata but does not say trumpet in the title or description.  When I drag the song from the search menu to a playlist and click on it the correct song will play. 
3) Some songs will refuse to play (iTunes claims that it is unable to find these songs).  I usually re-import from a CD when this occurs, which usually fixes the problem, but sometimes not.
4) Some songs were imported but do not exist in my library.  Most of these songs are accompaniment versions of other songs (background track only, with no vocals).  They have the same title as their counterpart, with "acc" added at the end.  At first I thought I simply neglected to import these tracks, but when I try to import just the ones I need they still disappear and I am unable to search for them by title (using the search bar) or by looking up their album.
5) Itunes will sometimes be unable to access tracks stored in the cloud, despite the computer having a strong internet connection.  I can download songs from the cloud using iTunes match, but this becomes problematic as I use more songs than I have room for on this (school-issued) computer.  I really don't want to spend time downloading and subsequently deleting files every week.

Answer 1

my home computer, where my library is stored, is running XP and it is not compatible with iMatch!
http://www.apple.com/itunes/download/:
iTunes 10.5 system requirements, Windows
Windows XP Service Pack 2 or later, 32-bit editions of Windows Vista, or 32-bit editions of Windows 7
I'm not sure how you're testing this with iMatch since Apple's site says it is not available yet, and there's no mention of any different system requirements (or any system requirements for that matter).
I don't know about the mp3 problem.  It might help if you provided a link to specific examples others could test.  I would think if this was a common issue with old mp3s there would have been 100,000 posts in this thread since it was started a month ago.