You need at least 15 or 21 days left on your current permitted to stay period. As you mention the last day is May 20th and today is May 8, the count is 12. Nothing to do with the way you entered Thailand. Leave Thailand, come back with new Visa Exempt Entry for 30 days and go the next morning to the Immigration Office for the conversion.
IF you apply for a VISA outside Thailand (On line or Embassy) you can be asked to show money on ANY bank account.
IF you apply for a VISA inside Thailand or an Extension of Temporary Stay at an Immigration Office you can be asked to show money on a Thai Bank account on your name.
The difference is where you apply and who's requirements you need to follow, that is why correct terminoligy is important to give advice.
You need to talk with your employer and see IF they are able to convert your Visa Exempt Entry into a Non Immigrant B visa at Immigration or if you have to apply at a Thai Embassy.
Your friend need also to apply for a Non Immigrant B visa, or Smart Visa or the LTR visa as the ED visa is employment prohibited, which simply means not allowed to work while being inside Thailand.
The only way to get an Extension of Stay based on medical reasons is with a doctor statement and hospital support.
So get him to a hospital and shout out before entry he has Covid, it seems amazing but hospitals, nurses and doctors know how to handle and how to put the patient in an safe area.
Only if you have resident status in Vietnam, otherwise you can not apply there for the Multiple Entry Tourist Visa.
AND the stamps in your passport and boarding passes do show you are not coming from home country, so fooling the system with fake VPN and fake tickets is not the best thing to do.