While I understand the dog question, I would forget about it until you have settled here.
You can enter for 60 days on a tourist exempt visa stamped in your passport on entry.
Concerning remote work, it is not permitted. Of course they turn a blind on short stays, but if you settle, there are a few (5 or 6) where people have been sent home for doing so.
Thai immigration are no different that Western immigration and starting to be far more strict because of abuse, mainly by the Russians, Israelis and Indians.
To be on the house book is down to the local administration and normally requires 4 months stay at the address and various recommendation letters, such as an official who knows you and live in the same sub district. But as I say, it depends on where you apply
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