You will be able to travel. Nothing has been mooted regarding how vaccination with affect entry requirements. You will still need visa/coe, preflight testing ASQ quarantine 15 nights, incl. post flight testing and insurance covid-19 $100,000 USD.
You are paying? Your name should be on the lease. There are immigration and TM30 reasons. Not to be cynical but..if your gals name is on the lease and you get in a big row who is gonna get kicked out then?
This has nothing to do with covid it is the medical needed for 0-A application (same for years). I need to get same in US and it will be costly. It requires licensed physician to record her medical license number, sign it, and preferably the clinics stamp. I got one in Chiang Mai this year for a few hundred baht but the certificate is only valid 3 months.
Yes, if you have the correct visa, COE, , $100, 000 USD covid insurance and every other requirement, and do 15 nights prepaid quarantine in an approved ASQ hotel.