I find that Etihad are awful on interlining luggage and generally don't want to help. It is usually down to the knowledge and experience of the person checking you in or their manager. I normally get 'it is impossible' or 'that is a different airline so how could we' etc etc even when calling BA's call center recently the woman made out that I was stupid for thinking it possible.

I still have a baggage tag from KHI with DXB MUS AUH DUS LHR on it thanks to an old hand knowing what he was doing. Horrible day in the air though !

Rechecking bags shouldn't take longer than about half an hour from deplaning

cannot help with the third sorry