Bench Power Supply for ESC and KV on motor
The ESC has a 35A requirements. With the bench power supply I have I can only go to 10A. If I am powering the ESC with this what are the risks? Over heating the supply?

The 35A specification means that the ESC can safely draw 35A from the supply.  The amount it actually draws will depend on the motor you drive with it, and the load you put on that motor.

I set the volts to 13v based on the 35A specs.

That's somewhat nonsensical.  Current depends on the load and the voltage, and you haven't tied those together yet.  You can have 35A at any voltage if you get to choose the load.

The motor stated 3600kv or 36v (if I understand correctly). Do I need to be concerned with this? The ESC manages that so as long as I manage the 35A the motor is fine. Why do I need to know this metric?

If you're deriving the 36V from the Kv = 3600 -- no.  Model airplane motors are rated in with a voltage to speed constant called Kv, which is in units of RPM/volt.  For a motor that's driven with \$v\$ volts p-p at the coils, it will turn \$v \cdot K_v\$ RPM.  That's pretty close to the speed it'll turn with \$v\$ applied to the battery terminals of the ESC and the ESC at full throttle.
Given that Kv rating, the motor is probably designed to run off of a single Li-Ion cell.  That's consistent with a propeller speed of a bit more than 10,000 RPM, which is typical.  12V with that Kv would be over 40,000 RPM -- I wouldn't attempt that without a scatter shield, or at least without making sure that there wasn't anything in the path of the debris when the motor explodes from centrifugal effects.