I would look at schools that do the visa for you... There is likely an additional charge or its part of the cost. If you're confused now you will most certainly be confused when trying something like and ED visa. Thai visas/Thai government is freaking nuts, in part because I don't speak the language, in part because the Thai government is little goofy (all governments really).
No limit for tourist visas. There is a limit on visa exemption by land (entering Thailand without visa).
You can get a re-entry permit at the airport on your way out. In my experience it takes 10-15 minutes but I try to fly off-peak times so you may want to allow a little more time.