AC recharge

Yes. Be careful of the amount, it should have a chart telling you add X amount to the system based on the amount of charge and oil. But if you need to charge the system anyway it is easier to just use a can of 134A with dye already in it. That way you get the correct dye, some oil and 134A all in one shot.

Sounds like you have a small leak or the system had enough air/moisture in it that some boiled off. If you pull it down to 29 will it hold for 45-60 minutes? If yes you can charge it and see how it performs. Keep in mind that all of the seals are designed to hold pressure, not vacuum, I've seen compressor shaft seals that leaked under vacuum that sealed good once in operation. If you want to check for leaks but don't want to waste 134A and the system is empty of 134A you could charge it with nitrogen or CLEAN, DRY shop air up to about 120-150 psi. Then use a simple soapy water and/or the UV light to look for any leaks.