See the big orange sticky at the top of the forum, entitled Texture Size, Pixel Counts, Video Memory, and File Formats? Read it. It's got a complete list of all allowable texture sizes.
In short, the answers to your questions are as follows:
1. The minimum dimension is 8, not 32.
2. Yes, textures can be any combination of allowable sizes, as long as neither dimension is less than 8 or greater than 1024. If you exceed that range, SL will resize the texture to fit its requirements at the time of upload, and the results are not always pretty.
3. Being divisible by 32 has nothing to do with it. It's all about powers of 2 (just like many things in computing). The number 32 just happens to be a power of two, so it's one of the allowable measurements, but it's not any kind of "unit" by which the other sizes are measured. All powers of two between 8 and 1024 are usable.
So, 8x1024 is fine, 64x512 is fine, 128x256 is fine, etc., etc., etc. Any combination of powers of two between 8 and 1024 is allowable. Try to do something like 2x1024 though, and SL will upsize it to 8x1024. Try to do 1024x2048, and SL will downsize it to 1024x1024. Try to use any number that is not a power of two, and SL will downsize it to the nearest power of two (unless it's less than 8, in which case it will be upsized to

.
Anyway, as I said, read the sticky. It's got lots of valuable information on the rules, and the consequences, of texture sizing.
Note: The texture size chart in the sticky has become a little hard to read since LL turned off bbCode on the forums. When I first wrote it, it was formatted in nice neat columns. As soon as they turned off bbCode, it became simple, unformatted text. Just now that in each line, the numbers on the left are the texture size, the number in the middle is the amount of video memory the texture uses if it's 32-bit, and the number on the right is how much it uses if it's 24-bit.