Ive just read the website again and can't see the reference of multiple entries using visa exempt so it may have changed when they changed it from 15 to 45 days. Regarding Hoi An I was meaning going there instead of Chiang Mai if borders were a problem.
There is a limitation on how soon you can re-enter. Check the UK website for Vietnam entry requirements. It might be better to fly down to Hoi An which is so nice.
I came on Qatar frim Manchester and no proof of onward flight required although there is a box to tick ssying you have all the required visa and associated stipulations covered. I did actually have a cheapo flight to Vietnam booked which i didnt use.
It depends on which immigration office you use. I transferred mine using Wise. If you select "funds for long term stay" as your reason for the transfer then it usually shows as coming from overseas but i believe its not guaranteed.