Wow, you should change your user name to "Twenty questions"

I see you spotted my older videos (galderdi). They were before I created the "Full Charge Motorsport" brand. And they were mostly with my old lead acid batteries.
Torque, well that is a difficult one. I have had a look at some of those BLDC motors and they seem to sit somewhere between 20 and 40 NM = 14.75 - 30 Ft Lbs but they don't say at what current. Torque is almost directly proportional to current (in the same motor). But I don't think it is correct to compare one motor to another, particularly diferent technologies.
Having said all that we can certainly consider some figures to understand some ballparks. DC motors a notorious for good torque figures. For my motor I have a graph that shows 10Ft/Lbs at 100amps and 150Ft/Lbs at 600amps.
As a side note, I am glad you prompted me with this question because by rechecking the graph from the manufacturer I note they have the maximum current at 800amps. So I think I will be hessitant to exceed that limit, although I suspect they are being conservative to rotect their product.
Back on subject, the peak power of my motor is 90Hp. If we assume it was a fair comparison and the performance is linear. My motor is roughly 4.5 times the capacity of yours. If I divide 150 Ft/Lbs by 4.5 I get 33 Ft/Lbs (only 3 above what I noted earlier). But I not 100% certain what that means for the current required to generate that torque. You are at 48V while I am at 144v nominal. Power is an easy calc but torque is more difficult. I suspect it is more about the current than the volts, so I suspect you will need about 130 amps to generate that 33 Ft/Lbs. Hopefully someone will chime in if I got this wrong because this is full of assumptions and guess work.
I think your gearbox will be fine. You don't have massive power or massive weight. What could possibly go wrong

What kills clutches and gears is suddenly dropping the clutch with an engine that is being reved. With electric cars that scenario doesn't make sense. We start with the motor at 0 revs and generally with the drive train engaged. So we don't get the sudden surges of power. To some degree this compensates for the high torque.
I don't have motor cooling. I only do 60 seconds of hard work (not even that hard for my motor), then it sits unused for 5-15 minutes. The motor temp is fine up to around 120-150 C. The heat does build through the day because each run adds heat faster than it can dissipate. But the hottest I have seen it is only about 50-60 C at the end of a hard day. I am going to add a small fan next weekend, but this is more about getting the hot air away from the controller than the motor.
The battery coolant is just plain Glycol coolant. Not sure if that is what I should use, but I haven't noticed any problems.
I can't remember the capacity of the coolant pump. But I really don't think it's important. It only needs to be strong enough to get the coolant moving, even if it is only slow. So long as the coolant moves the heat from the batteries to the radiator it's all good. looking on Ebay just now I think it was like 80-100PSI they seem to sell for around $30.
Hmmm they don't seem to use the same standard for cable here. Ours are quotes in square mm. However if current ratings are anything to go by they sound about the same (mine are rated to 350amp too). My cables are 50 square mm. The 350amp rating is pesimistic / nominal rating. In other words you can push 350amps through them continuously for prolonged periods. But you can push way more than that through them for short periods. Its all about heat. More current plus more time = more heat and eventually melting conductor. But a quick spike of current won't have time to build enough heat to cause a problem. I have run single 350amp cables from the battery to the controller then I have doubled the conductors from the controller to the motor (because higher current is possible there).
The tyres you refered to on Youtube are "R spec" street legal track tyres. Mine are specifically 205/50/15s. R spec tyres are around 30-100% more expensive than sporty tyres for the road but they litterally give 25% better grip (I can take the same corner in the same car 25% faster). For next weekend I have brand new slicks 250 wide with no tread. These should be awesome!!! Combined with ramping up my power should make my day really exciting.