Is there any instance in which, oe a possibility of, that an engine can play a novelty in a game?
Yes, once it is out of its opening book, it will just start looking for good moves. That will usually happen later than a human is out of his/her book, but still, it is not impossible that a human will (unintentionally) follow a certain existing game, where the computer will make the first deviation. And in a computer vs. computer match, they're bound to either replay an entire existing game, or one of them will play a novelty at some point in the game.
However, if you mean 'an opening novelty with any significance for actual play', the answer is probably no. Unless specifically configured that way, it will follow its book and not play a spontaneous novelty on move 12, like a human would be able to do.
Yes, and it's very common. Top players use the strongest engines to fine tune their opening books and new opening ideas. Lot's of ultra-sharp lines that you see played by top-ten players are home preparation, prepared by the engines. Although sharp, those lines are harmless (if you know how to play), the top players are confident because they have checked and played those lines with a computer, they know exactly what to do (eg: learn by being beaten) and how to make transition to the endgame.
Aren't all the moves after the book lines run their course a novelty? I make novelties all the time, though you might call them blunders, or too-unsound-to-be-played-again gambits.
Opening novelties don't mean jack. One night English champion Julian Hodgson showed up at our club in Hayward, Calif. He took on all comers at blitz, and one of the B players uncorked a genuine improvement in an Alapin Sicilian line — never been played before, as far as anyone could find, and it was better than the other moves that went before.
Did it matter one tiny bit? Of course not.