I have a Non B visa that expires in a few days. I paid for it and I have no contact with the sponsor any longer. They were taking too long to process a work permit so we parted our ways and they said they would not cancel it behind my back. But what I would like to know is if I can extend my Non B visa for one month (due to personal reasons) without having to get a document from the sponsor. I don't think it's possible, but I thought I would ask just in case.

You can only get an extension f you have a work permit. Unless you are married to a Thai or have a child with Thai nationality you only can get 7 days to get out of dodge.

If you do a border run you can get an extra 15 days by land, 30 if you return by air. A tourist visa from Laos would give you an extra 60 days.

So let's say I do a border run and return back on 12 Sept., would that give me to the 26th or the 27th? Would they count the 12th as one day?

Yes, the day you enter is day 1.