No vote is an option we've always had, it's just not voting, and we've been dealing with the nasty ramifications of the majority population "no voting" every election season (see: https://ballotpedia.org/List_of_current_members_of_the_U.S._...).
No, it's undervoting. Not voting (not casting a ballot at all) is very different from casting an empty ballot (or casting a vote of no confidence).
The difference is massive. Undervoting demonstrates active disaffection with all available candidates. Refraining from voting entirely demonstrates apathy (insufficient interest) towards the election at hand.
Yes, it is. Both write-in votes and undervotes are tracked. For example, this is how New York reports the certified results: http://vote.nyc.ny.us/html/results/results.shtml . Note that every write-in candidate is separately listed, including candidates who aren't even valid (Zephyr Teachout does not live in the 7th Congressional District, but two people wrote her in anyway). And the number of undervotes are separately listed as well.
Your local elections board/town clerk/etc. may present them differently, obviously, but they very much are required to track all votes, rather than simply ignoring all ballots that don't count towards one of the listed candidates.
A 3rd party vote despite the prevailing wisdom of them being wasted is slightly more resistant to these types of reductionist criticism, but still not as powerful as a "no confidence" vote would be.