I can not get it from the embassy. I'm not really emigrated (yet). So I'm still registred in Switzerland (home country) where I pay my taxes and where I have my insurance. As long as that is the case I can not get the letter from the embassy.
You're correct. You can enter by land twice per calendar year under visa exemption. Visa exemption can be extended by 30 days for 1900 Baht at any immigration office.
Get the application form in the building on the left. You can take pictures there if you don't have already (2 are needed). Wait in line, fill in the form and drop it off with your passport and the documents from school. Collect your passport the next afternoon at 1pm.
The multiple entry tourist visa is valid for 180 days and allows you up to 60 days (or 90 days when entended) per stay. You have to border bounce after that period (stamp out and in again).
You can enter before the visa expires and get another 60 days, which you can extend by 30 days to get a total stay of about 270 days with only two border bounces.
Visa exemption gives one 30 days for free and can be extended by 30 more days for 1900 Baht. So two land border crossing result in 120 days. Then you can fly out and in.
But if it was my goal to stay long, I would try to get a multi-entry-tourist visa or if that's not possible the single-entry tourist visa.