you missed the part when we started to say "use your own funds, don't need the agent" . . . or when we said, "you have no own funds, then use the agent to front them" . . . .
in the first case, you are fulfilling the first year's extension requirements which are that your own funds need to remain in your account for the full year.
However in the second case the agent just borrows you 800,000 THB and puts them into your Thai bank account for maybe 15 minutes, then withdraws them.
Which means that during the whole year of the first extension you don't have own funds sitting in your account, which further means you are theoretically in overstay, and further means you are not fulfilling the requirements, which require the funds to be remaining in your account during the year
not if you didn't keep your own 800,000 THB for three months after been issued the extension and respective 400,000 THB for the remaining year until 2 months before next application, in your Thai bank account for the whole year of the first extension. If you used an agent who put the money into your account for 15 minutes, you cannot apply for the next extension on your own
there is no calendar year count. The Immigration officers however check the stamp history of the recent 365 days. If you stayed on touristic entries longer than 180 days within the recent 365-days period, they will pull you aside at the border
that's not volunteering if you start working in and for a school this still is real "working", yet without payment. A school is not a NGO volunteer organisation or the Peace Corps. . . . . So it was a Non-Imm-B (employment) visa for you with documentation from the school, instead of a Non-Imm-V Volunteer Visa, and it doesn't matter if you get paid by the school or not
in case Immigration wants to see a certified by your embassy document telling them that you have been issued a new passport, try to evade it by politely saying that your embassy does not issue such a certification anymore (a new passport is a new passport!)
you need nothing but your old passport and the new passport. And maybe the printed TDAC to show (if it applies). Immigration will transfer only their own stamps - which in your case would be the "extension of stay permit" stamp and the re-entry permit stamp (in case you bought one). The "visa" itself cannot get transferred, the visa itself is a separate .pdf document. And if you entered on the new passport, the entry stamp will already be inside the new passport
this depends on the embassy where you apply through their E-Visa System. Some accept an up-to-date statement, others want to see 3 months of account statements, and others want to see 6 months of bank statements