If my distribution panel on my boat is wired 240 v 60 amps max and there are many 120 v 15 a circuits, if one side of the 120 v panel starts to draw more than 30 a, will the breaker compensate by adding amps from the low usage side of the panel ? to a max of 60 amps
No, that's not at all how it works.
This feeder will provide 60A @ 240V. That is 60A on each leg of the panel, NOT 30A on each.
The 60A is available, you use what you need up to roughly 60A, again, on each leg.
A residential panel will be hard pressed to be fully balanced, or greatly imbalanced, due to the transient nature of usage.
Depends on how the panel is wired. Domestic North American panels have each side wired in an A-B-A-B arrangement, so all the circuits on the left side do draw from both feeds.
But each (electrical) side is still independent, so you cannot draw more than the master breaker's rating on either bus. 240V / 60A usually means you have 2 x 120v feeds, each one up to 60A. The only connection between the two sides is the bar across the main breaker which ensures both sides go off if one side is overloaded.
If you have nuisance tripping of the main breaker you can very easily rearrange the circuits to balance the load. You will need a clamp-on ammeter to do this effectively, but they are not expensive.
And before you ask, removing the main breaker tie bar is not recommended. If you have zero 240V connections (no double breakers) then it is electrically fine to remove the tie bar. Wether local electrical codes allow it is another question.