You need to have a TM 30, Notification from House-Master, Owner or the Possessor of the Residence where Alien has Stayed, on file with immigration for your girlfriend’s residence when you stay there.
A re-entry permit allows you buy a permit to maintain your long-term visa status, which you have already paid for, by purchasing a permit that allows you to travel out of Thailand temporarily and return without losing your legal status on the long-term visa which you already paid for.
It’s a “Hey, I am coming back, so don’t invalidate my visa because I have left.”
meaning per calendar month, and any day in that month.
If your local office says something different, you can point out the regulation language or follow their made up interpretation if it is different from the rule.
Make it simple, your name only. Ask if the bank can designate your wife as the beneficiary of the account if you die.
If not, get a will, which is probably a good idea anyway. Things like designating her to decide your medical care if you are disabled and unable to decide yourself.