A year is not a long time
When the system is low on refrigerant, the compressor gets disabled to protect it. No need to jump it. Just clear the low refrigerant DTC to enable it just before recharging it.
What are your high and low side pressures?
You can warm the refrigerant can in hot water so the compressor can draw the refrigerant as a gas or turn it upside down and let it draw as a liquid.
It is possible, but only pressure readings will tell.
Not likely. As I said, it has a fail safe shut down to prevent just such a thing.
You are probably going to need an A/C shop with a "sniffer" to locate the leak or add a dye along with the recharge.