Vehicle Speed Sensor P0500 permanent code?

Permanent codes cannot be cleared using most scan tools, they have to be cleared by the vehicles systems after it has completed a set of drive cycles You can usually clear a pending or current code though. As far as the code you have, it will trigger limp mode. It basically means that the ABS system is either not seeing the signal from the sensor or that there is a fault in the dash or the ECM.
Does the tool you have allow you to see the wheel speeds from the sensors? If yes then look at those while you are moving, Say you are driving 25 and you see 3 wheels at 25 and one at zero that is where you start looking.
As for the no start, if you used a clear codes on some tools it erases all the stored values, that means it will reset the throttle and more. Try starting it with your foot barely on the throttle. Lets work on getting it running again first. Also, what tool are you using for codes? I'll look up it's specs to see what it can do.

Innova 5210. Does not have live ABS data that I'm aware of.

Yeah I it looks like it only does live engine data and can pull engine and ABS codes. Unfortunately that doesn't help in this issue. The issue is that although they say A, there is normally nothing that tells you which sensor is A because they use it as a blanket speed sensor code. As such you end up needing a scan tool that can read all of the sensors. Without it you are limited to checking the power and ground to the ABS module and visual inspection of each speed sensor. You could also use a meter to test for continuity but that won't uncover a bad harness or ABS module issue. There are shops that might be willing to connect their scan tool up and give you the results for a fee, then you could do the repair yourself. Or if you plan on keeping the vehicle a while and have others to deal with you could move up to a higher scan tool. Especially with all the sales at the moment there are some great deals out there.
As an example, a tool that is very capable like this used to be $1500.00

https://www.amazon.com/Autel-MK808BT-Diagnostic-Diagnosis-maxiCheck/dp/B07MBSZH48

If you look around there are some on sale for less.

Vehicle started and ran this morning in 24° temp up from 14° the previous day when it wouldn't start. Live data show TPS(17%), ECT(19°G and engine rpm while cranking(187 rpm).

19°F*

OK, good that it started, that won't solve the P0500 though. For that you will need a scan tool.