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Assuming this is your battery: https://www.renogy.com/deep-cycle-pure-gel-battery-12-volt-100ah/ There's a spec sheet on the Downloads tab. Charge voltage 14.2, float voltage 13.5. You could call or email Renogy as well, of course.

10ga is probably fine for the AC connection, but the DC connection between the battery and the inverter could carry 125A or more. I'd probably go 1/0, or even bigger.

Aren't headway 38120 cells 8Ah at 3.2V nominal? So your total capacity with only 8 cells would be about 200Wh, which is very small. Or is this just a proof of concept before buying a much larger batch of cells? Also, 10ga wire is far too small between a battery and a 3kVA inverter.