You have 3 months to use the visa from the date of issue, so either you're reading it incorrectly, you applied for it and got it 2 months ago and NZ post is atrocious. Or the embassy put the wrong date. Regardless, if you are stamped in on the 4th you can still get the extension even if the visa does expire on the 10th.
minimum age to get a language school ED visa is 15. That being said though, I know one person who couldn't get the ED visa for his son in Bangkok because he wasn't 16 but was able to get it in Chiang Mai so the age requirement may vary depending on Immigration Office.
1) if the landlord does the TM.30 online, they can file a new one from anywhere in the world.
2) you can try to ask for the login details and submit it yourself when the time comes. (Most landlords in my experience will happily give the details to submit yourself as it saves them having to do it)
3) If it's done in person instead of online, you can get all the documents filled in and signed now if they're still in the country. (I would suggest making the case for them to sign up online as it will be far easier in the future).
Regardless, so long as you've not moved or left the country since the original TM.30 submission, the original should be sufficient.
Have to be notarised too, but to my understanding the Ministry of Education will only accept them if they are authenticated by the Thailand Consulate/Embassy in the country the document was issued in.
For 30 day visa exemption, they can ask you to show proof of accommodation, an onwards travel ticket, and proof of funds (฿20,000). It all depends on the IO your facing at the time, how their day has gone/going and your history in Thailand as to whether they will or will not ask you for these things.
you should also factor in the exchange rate differences, not just the cost to transfer, not sure of the cost of the transfer from USD to THB, but GBP to THB the exchange rate differences makes it worth eating the extra cost to transfer as I still get more even with the extra cost.
the Non-O retirement 1 year extension requires 800k in the bank for 2 months prior to applying and 3 months after being given and to not drop below 400k for the remainder of the extension. With it being back up to 800k 2 months prior to applying for your next extension.