hvac control and ammeter

For current measurement You can use an Hall effect sensor like those produced by LEM. Its only necessary to pass a single mains wire (phase) into a hole... bye delo

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Yes, but that breaker does not trip instantaneously, there is a delay. The relay/switch whatever in the tstat supplies that current instantaneously.

Don't bother trying to monitor it, it can vary greatly depending on operating conditions like start-up counter-torque from whatever the motor is driving.

Only if your motor loading is < 1/3HP...

The relay may even require that inductive spark to preserve its contact material, don't worry about it.

Amperes Full Load

Duh

Don't do it. If this were your own home, I'd still suggest that you not mess around with the wiring. But as you are likely to burn down the homes of other renters as well as your own, this is all the more a bad idea.

AC current is typically measured using something called a current transformer. They have a side benefit of providing isolation between the high voltage circuit being monitored and the monitoring equipment connected to their secondary (which I can already visualize bursting into flames).

It appears to be OK.

AFL = Amps Full Load

If a device has a horsepower rating, that indicates that it is suitable for use with a motor up to that size.

Usually the rotor is not locked on a motor :-)

If you do that for more than a few seconds three things can happen. Either the circuit breaker pops, or the thermoswitch begins to cycle, or smoke billows out of the motor.

You can use a clamp meter. Contactless. You open the clamp and then close it around one of the motor wires (not both). Harborfreight has meters like that for little money, don't know how good they are.

That relay sound a bit wimpy for that purpose. At least for my taste.

WRT horses I've seen rather bizarre statements for motors that sure sounded like the marketing guys had gussied them up a bit.

Who decided that the HVAC was to be connected on the same wiring circuit as domestic lighting? GPO's and lighting should be on individual circuits as should HVAC. Having HVAC on the same circuit as lighting is simply a disaster waiting to happen.

would

sufficient?

This is the tstat