4 layer PCB stackup for motor control board suggestion
You are using a standard 35µm 4-layer stackup, which is fine. Signal/power/power/signal is also quite common. Digital and analog plane on the same layer is fine even without lot of separation.
Now, for the questions: the control board is often separate (plugged in vertical in many design) to better isolate the controller from the switching noise. Also with heavier copper you need greater clearance so you couldn't solder a fine pitch controller: already at 70µm copper clearance become 0.2mm so a 0.5mm pitch component starts to be problematic. If you can fit your controller/drivers on the main board it's simply cheaper (one board less to make)
Lots of vias: you are talking about thermal vias: they spread the heat between planes. For a price they also can fill them with thermal compound. The 'lots' is really an empirical issue. I use 2-2.5mm spacing for example with 0.3mm vias. There is some literature on the effectiveness of thermal vias but it's trial and error most of the time. If you are rich there is thermal simulation software, never used it however.
1.6mm is the typical thickness of the board. Yes, usually vias go from top to bottom unless you are doing high density interconnects with blinds and embedded vias. Very expensive, don't even think about them. The value could be useful for estimating via inductance but I don't think it's needed in this application. I simply never heard talking about via height…
Thermal relief for MOSFETs depends on your assembly process. It's a compromise: without relief you have better dissipation but it can be problematic to solder them properly. Most of the time is better to relief the pads. Also remember to reduce the paste area from the big pads to avoid outgassing issues: the datasheet should give indication for that (often for thermal vias too).
As for the trace width/clearance: you didn't specify the single most important parameter for spacing, the working voltage. There are tables with clearance and creepage to be used. If it's a very low voltage motor it seems fine. As for the trace width you have to decide how much the board can heat up: it depends on the enviroment and other things. For 5A 2mm is usually enough, you can find the calculators on the net. The bigger the better anyway. For the 100A surge it's more difficult, it depends on the surge 'shape' (you literally have to integrate the energy to find out)