MOT Power supply issues

1. The problem with MOTs is the voltage is too low to make a sparkgap work reliably. A pair is just-about doable but still not ideal. A neon-sign transformer is an easier and safer transformer for a first-time coil.
2. Insulation and /or spacing
3. A ground with a low inductance path, and one that will not damage anything if it sees a HV discharge to it. i.e. not the ground pin on an AC outlet. Stake in the ground is ideal as long as the cable length isn't very long.
4. You won't need to do any measuraments on the HV side. You will know if there is HV present - corona hiss, ozone smell, arc-overs etc.

The quality or limit to current in the secondary will be based on the ESR of Ct and Primary of Tesla coil. Tesla's patent, indicated only use high quality Mica Capacitor material

My recommendation;

Ditch the ceramic cap and look for high quality mica material or cap made from same.

Get a platinum tip automotive sparkplug which should arc at 8kV in air or adjust gap to desired protection level. Keep in mind that ionization has a time lag and overvoltage will occur before air gap protects the capacitor. Consider using spark plugs for all your gaps and tune the gap for the desired breakdown voltage.

The ESR of the gap will drop with rising current due to current density. This has a negative differential resistance and the value of this negative ESR also limits current, where a very low negative ESR generates very high V = L di/dt into the coil.

Higher Resonant frequency is better and just as important as ESR of all the elements in the Tesla primary coil loop.

So ideal is ESR is infinite with open gap and 0 Ohm during ionization, thus di/dt becomes infinite. In practise di/dt is limited by stray capacitance and self capacitance of Tesla coil( which determines self resonant frequency (2PI*f)^2=1/LC (impulse response will show this on floating scope probe shunted to ground clip as a small a loop antenna) and I is limited by ESR or effective series resistance. For better scope results use 1 turn coil around current path and terminate 50 Ohm coax with 50 Ohms at scope. THis will yield rise times of <1ns and low voltage into 50 Ohms from which you can now calculate power of the pulse as V^2/50*t, where t= PW50

So in summary, high self resonant frequency coil and low ESR mica caps and spark plug protect any caps used to prevent failure ( which results in carbon trees)

A poor substitute for Mica may be thick film Plastic like Polyester, Polyurethane which are expensive much better than ceramic for ESR and leakage. (Edit, Your MOT caps are probably one of these. the second stage Tesla air core step up transformer with the Donut terminal on top for reducing E-field gradients ought to extend your arcs to 10x what you are getting now from the MOT. If you create a free-space antenna grid you can also capture energy from static electrification and generate even greater energy pulses with a resonant pulse and single panel antenna grid as air gap capacitor to earth >10m below) If you perfect this, you might even get it to self resonate sustained arcs without 120Vac ;)