Ok so, here is how to process went for me:

Golden tip: First things first, download the Dubai Police app, next, tap the fines button. Now, type in the car you're interested to buy's number plate number, Letter, registration type (private, classic or expo or other), its emirate. and then hit submit.

The app will show you the fines against this number plate. This will give you some idea on how to car was driven in the last six months. Was this guy always getting parking fines? was he speeding in it? did he pay his fines on time?

Ofcourse, all will be reset once you get new number plate, but this back ground check will give you some idea on how the car was driven.

1. Agreed on price with seller.
2. Went to RTA (the one next to Dubai court in Al Barsha. next to gold and diamond park)
3. Had the car tested by RTA (there are two choices, normal one, that you described in point 4, and the "comprehensive test", will explain about it to you in a moment, keep reading.)
4. Took result from Testing and then me and owner went to arrange insurance (RTA offices have insurance companies inside). Chose full insurance of me and passenger.
5. Gave necessary documents for transfer of ownership, (my passport, emirates id, driving license, insurance that i just bought, owners gave his passport, emirates id). The car is now mine.
6. went to number plate table, got number plate.
7. Went to Salik, and bought new Salik Tag.
8. screwed off old number plate, put on new one, took off old salik, put new one.

RTA comprehensive test: This test is more reliable, and actionable than that from a private mechanic. This test costs more than normal ~ 250 AED. But it is from RTA, RTA are the Dubai Govt. Think about it. I suggest you have this done.