I would happily live with my conscience if it means not going to immigration every time I go and visit another province. Why do more than you need to. I am not sure about Phuket, but it is not enforced in most other places. Also you really only need to register the TM 30 if you will be going into an office for an extension or other reason. Otherwise if not visiting an office, there will be no fines or consequences.
Dan Goodwin 20k THB cash or same in other currency, proof of accommodation and flights out of Thailand. These may NOT be asked for, but any or all can be asked for at any time, especially if the IO wants to question the reason for your entry into Thailand.
It will depend on the IO on the day as there is no rule or limit to entries by air on Visa exemptions or tourist visas. Have 3 proofs as Robert recommended.
Getting a new passport to 'erase' any previous entries went out the window the moment they out everything online. 6 month visa is a good recommendation for a long stay and mutiple entries.
A Yes. B Yes. C Yes. Everything is online. New passport has zero affect on entry into Thailand. The only affect it has is for applying for visas in neighbouring countries as they do not have an online database.