Unless she is trying to hunt you down to kill you, go ahead. What do you have to lose?
Yes you should
Sure. What harm could it do?
If she told you she didn't want to hear from you again, then no. Otherwise, just a simple card would be nice, and she can choose to respond or not.
yes, maybe you can make up
Depends on the not so good terms, if it isn't something that would offend them then I would send it.
But don't add any particularly personal message. If she wants to find out how you're doing she can.
If it isn't disrespecting her wishes, and it's something that you want to do, then do it.
Yes, regardless of her reaction, that still makes you the better person...