1. You're on a visa exempt entry, tourist visas are 60-90 days.
2. You don't need a tm6 anymore, they've suspended them.
3. Yes, you need a tm30 receipt. If you're staying in a hotel, hotels do them online. Ask for a printout of the screen shot from them or take a picture of the receipt with your phone and print it out.
If you just want to stay in Thailand, will be cheaper to buy a 60 day tourist visa before you come compared to going to another country or doing an in country extension.
If you want to force yourself to travel a bit, cambodia, Malaysia, and Vietnam are all open and easy to travel too