How can I seal a slate floor for long term protection?
If you're regrouting I highly recommend epoxy grout.  It's impermeable and doesn't have to be sealed.  I'm never using regular grout again.  I've done some myself, and have also asked pro tile setters to use it even if they haven't before, and haven't had problems with that.

Here's the post that turned me on to it for more info on market options