I don't know where you got that statement from. It is exactly the contrary, false positive doesn't exist, but you can have the virus and be tested negative because you didn't get enough material on the swab or the virus wasn't virulent yet when you got tested.
Every house has a blue book. One house number = one book. Then if Thai nationals decide to live officially in that house, their names will be written in the blue book. If foreigners decide to live in that house, they will put their names on a yellow copy of the blue book.
Your name is at the end of the blue book as owner of the house. But you are not listed in the book as living in that house (with ID number, birth date, nationality and parent names). If you want to be a householder, they will give you a yellow book.
If you apply for a new visa, the money can be/is supposed to be in a bank account out of Thailand. The 2 month in a Thai account rule is for people changing their visa type inside Thailand.