it's easier at home than it is in Thailand. Especially since you have to have a Thai bank account or embassy certified income to apply in Thailand and you cannot get a bank account without already having a long term visa. So that means agent is the only option for the bank account
There is no limit. But that doesn't mean it's unlimited. It's much more about how long you've been in Thailand than it is about how many times you've entered. Around 90 days in the past 6 months they start to interrogate you. Around 5-6 months in the last year or so and you're looking at possibly being denied entry. A tourist visa isn't likely to help if it's gotten to that point.
TM30 is a legal requirement for EVERY property owner to do within 24 hours of arrival at that address. If you've stayed at a hotel you have a TM30. Ask your landlord or hotel reception for a copy. You cannot do a 90 day report without having a TM30. It literally has nothing to do with your visa type.
You can apply for a 30 day extension each time you enter. Or you can apply for a tourist visa from the Thai embassy before you travel which will give you 60 days when you arrive.
But right now no one knows if or when visa exempt will switch to 30 days.