You won't need the surge protector for a inverter type gen. You need to provide more info on your a/c unit. It may or may not run on the 2000. Single high wattage items like hair dryers and coffee makers are usually the cause of tripped breakers. You always have to consider what else is using the power at the time. You won't damage most things but the a/c unit could be another story. I have a 3000 watt gen and my automatic fridge keeps tripping my memory about the time it trips a breaker, if get carried away with the microwave and a/c.
Your trailer will be trying to recharge the battery as soon as your start the gen. You might have to start the gen early so the battery can absorb some of the life giving nectar then let other items have their share. The converter will always run unless you turn off the breaker that supplies it's power. If you have a 3 stage converter it uses max power at first. This means a 45 amp converter could use half the power from the 2000 until it kicks down to the second stage. We seem to use more juice than think. It's a learning experience. The Honda 2000 is a very good choice as long as it is capable of running thing you need.