I would look and make sure your condenser fan is coming on. If it isn't, that would explain why it only cools when you're moving. Assuming you have a low-pressure safety cut-out in the system, cooling would actually get worse the faster the compressor spins, as the pressures & temps would get lower.

Yes, it's called a pressure-temperature chart or PT chart. You should be able to google one.

If it's currently holding gas, you should just add more & not crack the system open.

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A.S.E Tech A1,A6,A7,A8 & MVAC 609 + EPA 608

Unless stated otherwise, any question I ask is about my greymarket 1985 380SEL.