You have come to the right forum! :)
So first give us the brand and model of the 35 amp converter so we can know how it gets its 120v. Some you just plug in and others are "hardwired".
A 35 amp converter means only 35 amps DC. Its 120v input requires only a 15a circuit.
On your 120v breaker panel, there should be one marked "CON" that might be sharing with some other 120v thing like "Receptacles" If the converter has its own breaker, that can be the switch.
Your "gel" batteries are probably AGMs. There is a difference in how to recharge them. Confirm what you have there.
Two 100ah batteries are not enough to run that 2500w inverter to run anything big like a microwave. OK for TV sets etc. Needs two more batteries for a MW.
600w of solar is a lot with only two batteries as "storage". You can recharge them quicker than four batteries, but then you can't last as long between sunny days. (As is the situation)
