That’s going to be specific to the office you use. Some will require it, some don’t seem to care. If you specify what office others may be able to advise their policy.
The amount of documents that are needed to apply for a Non B in country is huge and most companies can’t provide all that’s needed, therefore it’s way easier to provide a few documents that are needed for a non B application outside of Thailand.
What documents that would be required is dependent on the embassy you’re going to use, and the documents need to addressed to them specifically. Check their website for requirements.
On a Non OA you will stamped in for 365 days on each entry or up until your insurance is valid until. If you enter just before the visa expires and have the relevant insurance you’ll still get the full year. This “second” year is not multiple entry. If you want to keep the stamp “alive” you’d need to get a re-entry permit (single or multiple).
No one knows how many exempt entries you’ll get away with as it’s up to the individual immigration officer you hand your passport to. Perhaps two maybe eight who knows.