In my states scantron era... I don't know... If you walk up with a ballot that you have not scanned and spoiled in some way... I would assume... they record destroying the bad one and give you another go... Once it enters the scanner... finished..
Yup. If you marked it wrong, you "spoil" that one and get a new one (subject to a max of 3 tries).
If it won't go in the scantron (keeps getting pushed back) you get to keep trying until it works (the voter is the only one handling the ballot). But once accepted your vote is "cast" and you are done.
On the privacy at home voting thing, you have an envelope for the ballot that goes in the mailing envelope. So I guess you could vote your conscience and then seal it up so your spouse can't get eyes on it...