Can Feedback be left when a buyer doesn't complete a purchase?

More than likely they can leave feedback. I would wait for then to do so and then leave feedback on them but remember feedback has to be posted within 45 days of auction ending, If you feel their feedback is unfair you can request Trade Me to withdraw their feedback

Yes they can still give feedback. But If they ignored all other emails via TM, like payment instructions & refund requested, then they'll prob ignore the 'place feedback' one too. But you never know. Expect something retaliatory if you do place anything yourself

To be more specific:
Can a buyer who doesn’t complete a purchase or answer emails or respond to TradeMe leave negative feedback?

Yes they can.

So I can place a bid on an auction, win the auction, change my mind, not follow through and make payment, ignore all attempts at communication from the seller and TradeMe, not suffer any consequences and still get the opportunity to place retaliatory feedback?

Yes, but you are not allowed to place retaliatory feedback so when you do, the other member can ask Trademe to remove it as it breaks their feedback policy. You can place negative feedback, but just make sure it doesn't break Trademe's feedback policy and is not retaliatory.

Another example of why the feedback doesn't work as intended. Facebook did have the same issue, but they changed their feedback, so now you can't leave negative feedback for tyre kickers & time wasters. You are encouraged to report them for droping communication or not completing trades. After X reports, they get banned from marketplace.

If I post feedback, then buyer with whom I have had no contact buyer can post feedback on me. This stops fair feedback. I should be able to say the sale did not go ahead and post a negative emoji. However I know if I do that the "buyer" will post baseless negative feedback about me. Once the success refund has been credited the buyer should not be able to post feedback on me. I note the buyer has similar feedback, but the person posted a smilie face so as not get incur the negative feedback.

TradeMe is an essential quality question.

It's fine if they can post a response to my feedback on their own feedback site but unfair and prohibiting on openness if they can give feedback on me.

The feedback system could be a lot more accurate.
I checked out a member who had a 98% feedback rating but after investigating I found they had 15 incomplete purchases yet none of those had anything but a smiley face.
If I am about to trade with someone I think it's important to know that out of 100 trades, they didn't 'follow through' 15 times - without having to wade through all of their feedback to find that out!