if your /var directory is on its own partition, you may be able to leave that unscathed, but you could copy it all as root and then replace mint's one with your old.
If you want to keep all your software, try AptToCD (not sure of the url, youd have to google it)
I doubt you'd have any issues sharing the home folder, although, tbh, if you have ubuntu working fine, I wouldn't bother with the switch, unless you are finding it a real pain to get the media codecs working.
sorry if that made no sense, I'm a mint noob myself, but know a fair bit about linux, but I hope it was helpful.
*edit* in answer to your 3rd question, probably, since they are essentially, deep down, in the basic code and stuff, the same distro, one being an offshoot of the other, but since there is a vast resource of knowledgeable users here, you might be able to get your info from here instead.