To reason about this, consider applying ohm's law to the line leading into your house. It's not possible for the voltage to be higher on the house side than the grid size by more than an amount determined by the resistance of the wire, which is going to be very small. Probably tens to hundreds of milivolts.
Current flow is limited by power output. I have a 3.8kW solar system in the UK which outputs up to the 16A mentioned in the other comment. It occupies my entire roof, and is just below the 4kW limit to which a different permitting and feed-in-tariff regime applies at which point it would be an "industrial" system.
100A on a US 110V system would be 11kW, quite a substantial system costing in the region of $15k.
Obviously no permitting regime is going to let you put a >100A output system on a 100A line as that would melt the line.
- Hard to tell, although I expect it would be cleaner. You might be able to pick up a harmonic output from the inverter, showing as a slight ripple in the sine wave. It's certainly obliged to be the same frequency and RMS voltage.
Edit: I have a grid-tie system in the UK, so can't really speak about US grid or code matters.