I believe in both cases, and as exampled by Tod, it is full calender months, not accumatilive days (equating to an average month), therefore March 1st.
But make sure you wait to apply for it after the consideration period and you have received the extension stamp. Dont do it when first submitting your documents.
you said they dont ask for tm30 at Patong IO, (this could imply its not required to exist), unless the office has a local requirement to attach a hard copy of the tm30 to your extension form for filing, the fact they can see it on their screen suffices the need to ask for ask to see a copy, hence they don't ask. If there isn't an active one filed in the system they will ask.
as you were there 75 minutes, you were probably sitting in the waiting room for most of that where the Thai version of the video is usually on a constant loop and covers the requirement for Thais. My last 5 year one i did the online video at home, got the qr code and was in and out of the dlt within half an hour, didn't even get to sit in the waiting area, which wasn't by any means empty of locals.
The online system is just the tool that hotels and now householders use to record your arrival, and it creates a tm30 record. The hotel you are currently staying should have recorded your arrival (and length of proposed stay). You should ask them for a copy. They may need to re-enter your arrival, as copies are only printable for 7 days, so don't worry if the arrival date on the form isn't your actual one.
if you have a visa, when you arrive at passport control, technically your saying 'i've been given permission by your foreign office to enter the country, if everything is OK, can I enter'?
While a visa exemption is saying ' please can you check if i am able to enter the country'.
With a visa the majority of the IM's job is done for them, and its pretty much just a stamping exercise. Without a visa your 100% in the hands of the IM to look at your travel history and for them to decide wether you fit the tourist criteria.