What are the rules for the 30-day entry into Thailand and re-entering for another 30-day exemption?

Why not do the right thing and apply for a tourist visa from your home country. Cheaper and not a lot of hassle with borderline and imigration

1) no. Depending on your passport you receive a 30 day visa exemption. You do not get a visa.

2) you can extend the visa exemption at any immigration office in Thailand for another 30 days for 1900 baht. If you depart Thailand and return you would receive yet another 30 days which can be extended 30 days

Yes

There is no such thing as a 30 day visa.

If you are from a country eligible, and arrive without a visa, you can receive a 30 day visa exempt stamp (not a visa, it means you are exempt from needing a visa)

If you want additional time you can go to immigration and apply one time for a 30-day extension.

Or if you leave Thailand and return, you will receive another 30 day visa exempt stamp.

You can only leave and return at a land border without a visa 2 times per calendar year. There is no limit written into law about how many times you can do this by plane, but you cannot do it to stay in Thailand long term.