What is the usual or maximum speed during the push-back procedure of large commercial aircraft (say, B737, B787)? Is it fixed or dependent on the aircraft type or weight or anything else? Is it different for towbarless vs. towbar procedures?
There is no regulatory guidance on how fast (or how slow) an aircraft must move during the pushback. Furthermore, there are many opinions (see below) on how fast an airplane moves during pushback.
If you watch a pushback, you will notice that ground personnel known as wing-walkers* will walk alongside the aircraft, at the wingtip, during pushback. The normal speed of humans walking is 3-4 mph, which can surge to 5-6 mph for short distance.
The speed is not fixed. It is dependent on all the factors you mentioned plus the experience of the tug driver and ground crew as well as size of the airplane and its weight. It takes longer to accelerate a large airplane to this speed, and it is harder to slow down a large airplane.
* ICAO Annex 2 Volume 5 (Appendix 1-5) and SA CATS 91.05.1 (5)