I took it from the post you were just asking about re entering Thailand. Sorry I cannot answer your question on visiting Goverment Offices in remote areas as I have not had to do that so would only be guessing.
But I imagine if you have left with no exit stamp and then re entered so have new entry stamp they will see all is in order but that is only my opinion.
Nope first time I exited through auto gates I did wonder if anything would be said on my return about no exit stamp. On my actual return nothing said allowed to enter as normal so its obviously in the system and works
In 20 yrs of visiting a minimum of 3 times a year I never been asked for proof of return/onward travel tickets nor proof of accomodation whilst there.
The first few years I just turned up on a one way ticket with no accomodation arranged and just travelled about till I decided where to go next. I am a bit more organised now but never been asked