Can I still use the same characters

Without re-registering?

As long as those characters were the last ones you used, sure. There's no expiration date on them.

It's possible, and likely, that you will have to make some minor updates to reflect new rules.

I believe that the biggest change while I was gone was buster damage. (well, that and the Great Net War, but I'm not getting involved in that) Am I right?

Oh no, there's been a complete revamp of the sig system too

Saw that. Check the registration forum. Should I make a new topic in Electown before I go onto the net?

Assuming you don't have a battle sitting idle somewhere, you should be able to start a new topic right away.