Los mexicanos no necesitan visa on arrival desde julio de 2024 (antes sí). Ahora, con solo el pasaporte, al llegar, te sellan un permiso de estadía con exención de visa por 60 días. Dentro de Tailandia se puede extender a 30 días más (90 en total), pero hay que pagar. La visa on arrival aún sigue siendo obligatoria para OTROS países, y para ellos, en el aeropuerto se hace una fila diferente, hay que llenar unos papeles, entregar una foto tamaño pasaporte y pagar 1.900 o 2.000 (no recuerdo) bath en efectivo. O sea, lo mismo que tenían que hacer los mexicanos hasta antes de julio.
Ask directly to the Embassy. My visa was issued on a public national holiday of the host country, which obviously wasn't observed by the Embassy (they worked as usual). Said so, my Embassy has on its website the calendar of closed days, which include all of the Thai public holidays and SOME but not all of the holidays of the host country.
No, you don't need to go to Turkey. It means that the Embassy in Turkey is concurrent and in charge of other small countries. That's common. The Thai Embassy in Chile is in charge of Costa Rica. Also, both the Embassy in Mexico and Peru are in charge of other countries, as those three are the sole Thai embassies in Latin America.