I have not been to DMM recently but do fly into KSA quite often.

1. Yes, you can have dinner in the lounge before sleeping in the airside hotel

2. Passport control in KSA is slow and inefficient. Nothing scary, just slow and inefficient. DMM is not known for its tourism industry so don't expect to be warmly greeted. Be prepared to queue and wait - it's better to just set your expectations that way so that you'll feel good if things move quickly (which they may - it really depends if a large flight arrived before you). As a first time entry on your visa you will need to do biometrics at the counter (photo/finger prints). You will see some people run - don't be alarmed, they are just running to queue. I would recommend you move briskly so as to not be stuck all the way in the back. Sometimes the queues can be different for "first time on visa" and "reentry" although, of course, it won't be clear and definitely not posted. Ask someone in the queue. The posted queue signs for "business men, residents, etc" are mostly meaningless except for the "GCC Nationals" one.

After passport control, get your luggage if you have any. You will have to scan your checked and carry on luggage before exiting customs... (ie don't bring alcohol with you).

3. Departures are a bit of a scrum in KSA.

As a Gold, head to the Emirates J line at check-in, but that's where it ends. Don't remember if there is lounge access for Gold Y in DMM. At the gate, it's typically a free-for-all and boarding by class is often ignored, let alone skywards tier recognition. If you don't have much carry-on, consider waiting for the masses to board and get on last.

Hope this helps!