Many condos will do it for you, but you have to go down to the office and request it. That can be a problem if the rental agreement is not legit (that's a whole other conversation).
" tourist visa is 30 days free entry" You're confusing Visa with Visa Exempt (welcome to Thailand).
Visa Exempt - you are given permission to stay without a pre-approved visa. The duration of your permission to stay depends on your nationality.
Visa - you process paperwork at a Thai Embassy outside of Thailand. They give you permission to visit.. This 'permission' is non-binding, the immigration officer can still refuse you entry, but very unlikely. Your permission to stay is the stamp the IO puts in your passport, the duration depends on your Visa.
Border run will do. I live in Pattaya and there are agents that will run you to Cambodia. Round trip 3500 - takes about 8 hours. Flights will likely cost a little more and take a bit longer (taxi, wait at the airport there and back, etc, etc).
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).