The hum is probably the load on the battery charger portion of the inverter. If it is loud initially, it is likely because the batteries are low and it is pumping a lot of juice into them. There is also a thermostatically controlled fan on the inverter to cool it if needed. Some inverters are noisier than others, though. I sometimes notice mine when it is real quite too, and yours being in the garage probably amplifies it.
I had one inverter get noisy and it failed 3-4 months later. It was rebuilt - all new electronics inside - but after the rebuild it was always noisier than the original. It's been running 1.5 years now, though.
The inverter doesn't know anything about 30A vs 50A. I suspect you are referring to a display from the Intellitec EMS system, which shows what type of shore power (or generator) is available and what loads may have been shed if power is limited. It should respond immediately to what it sees, but your shore connection may have a built-in power monitor that checks for things like low voltage and improper grounds or neutrals. Some of those take 30-90 seconds to sample everything before they allow power through to the coach, which would include the EMS system. It may also include a start-up delay to protect the a/c units from a flutter in the power input. The one I have now is very slow, more than a minute, while its predecessor was only about 15 seconds. Maybe it is doing a better job???