Is there a grace period to leave Thailand after a 30-day visa exemption stamp?

There is no grace period for overstay. You may mean that IF you fly out from airport the fine will be waived for one day when overstating is less than 24hours. Overstay fine for 1day (500 baht) would be waived, but you still get stamped as overstayed. Especially if you are thinking about getting SETV in Vientiane, overstay even 1day doesn’t seem to be very good idea...

Leave Thailand before 23:59 on 4th Aug, or go to immigration office to get 30days extension (or 7 days extension denied stamp if you already applied and got 30 days extension to original visa exempt entry) if you want to stay a few days longer..

No - you have until 23:59 on the 4th -after that you're on overstay - depending on how/ where you leave there are different repercussions.

No. The immigration officer, at their discretion, may not charge you a fine for one day overstay but your passport will still be marked as overstay.

No. No matter what nations passport.