Marking answers as "the correct answer" is entirely optional. While many community members really want question askers to mark answers (especially their own, because they need that rep) the community as a whole has more of a problem with those badgering the OP to accept than with people not accepting answers. Yes, it's nice when they accept an answer, but if they don't it's not all that big of a deal.
As to not providing any feedback at all, that depends. It's certainly possible that one or more of the answers provided were helpful, the OP upvoted them, solved their problem, and then went on their way. That is absolutely fine. Again, accepting an answer is good, but not doing so isn't bad. Commenting on posts with things like "thanks" "that helped" or "this was the solution I used" are considered comments that the community doesn't find constructive or helpful. The first two should just be upvotes, and the last one an accept.
What's more of a problem is when the OP does not respond at all to comments requesting clarification on the question, requests for additional information, or don't comment with a good explanation of why unhelpful answers don't solve their problem (whether it just doesn't work, or doesn't solve the right problem).
As to deleting your own answer, I feel that if an answer is heavily downvoted it ought to be deleted. It is the communities way of saying, "This answer is more harmful than helpful." To me that means that it would be beneficial to have that [bad] information not there at all. The fact that it's removing the negative rep from you is actually an incentive towards this behavior. When I downvote an answer that's really bad I'm hoping that the answer is deleted (if I didn't hope that, I wouldn't downvote). When I downvote I"m not trying to say, "you really need to lose 2 rep for being a horrible person" I'm saying, "I think this answer is actively harmful and should be deleted, please either fix it or remove it or face the wrath of my -2 rep."