I dont know if it will complicate anything removing the mechanical brake from the motor. Might just disable it and leave it in place. I dont think it would have any effect on motor cooling.
I do agree the brake resistor is pretty straight forward.
Now trying to wrap my head around relays, interlocks, fuses, and breakers. Where and when to use them.
When you make a final determination on the VFD you are going to use, check out the manual. They will probably give you a recommended wiring diagram for input power as well as the DC signal wiring.
Let's look at the WJ200 you commented about earlier as an example. On page XV (PDF pg 16), they recommend a fuse rating for Class J fuses. These will be sized for the full load available for the particular size drive you select.
Page 2-4 (PDF page 49) offers the best look at the system layout and provides the diagram below.
You do not need all of this for a basic installation. At a minimum you will need a breaker or fuses for the input power for the drive, you may want an AC line filter/reactor (will discuss more), and a braking resistor.
Let's look at what I would assume your system would be. Your motor is 3HP (2.2kW) so I would think you should select a WJ200-022SF (assuming single phase power). Then using their fusing table, you would select a 30A AIC 200kA fuse (Class J). Note that this is higher than 8.8A because we are fusing the single phase line into the VFD. If you wanted to use a breaker, make sure you are using one rated for motor loads. A 30A trip curve C should be sufficient for this low starting load application. For 240V single phase, you would use a 2 pole breaker or fuses since both lines are hot relative to ground. You would need to run at a minimum 10 AWG wire (NEC 310.15(B)(16) and manual page 2-16 (PDF page 61)) between the breaker/fuse to carry the 30A.
I would highly recommend a shielded "VFD" cable for the motor output. VFDs create extremely fast and high amplitude power switching which radiates as electromagnetic noise. Using a shielded cable can help prevent this from messing with other electronics in your shop. 16 AWG would be sufficient for your motor, but I personally would do 14 AWG.
With an appropriate braking resistor, you can achieve 100% of motor rated torque to brake the load.
A line reactor or line filter on the AC line side of the drive will provide more stable power for the motor and help prevent the drive from reflecting harmonics back onto the AC line which can mess with other electronics plugged into your house. Here is one appropriately sized for your application. This goes between the fuses/breaker and the drive.
For your application I would not recommend filtering on the output of the drive.
Proper grounding and HF bonding are critical for VFD applications. You should bring all grounds back to a central location shared by the utility ground wire. The drive should be mounted on an unpainted subpanel and the subpanel should have a solid ground back to the central point. The drive should be in a metal enclosure and the enclosure and door should have separate grounds coming back to the central point.
Alarm wiring and DC signal wiring can be discussed later, but they recommend 18 AWG stranded conductors (suggest MTW wire). You can share what your signal connection requirements are and I can try to help you out.