You are correct about the process and there are some here who claim the CO2 does nothing at all, but an argument you frequently see here is that there is no, or almost no positive feedback. A significant portion of equilibrium climate sensitivity (ECS) is the positive feedback that any temperature increase will receive from added water vapor that higher temps put in to the air. Of course no one has ever explained why there WOULDN'T be such feedback but there you go.
Yes
On the order of a couple centuries.
Scientists have made estimates and they are all in that ballpark for CO2. Methane, which absorbs more IR than CO2, fortunately has a shorter atmospheric lifespan of about 12 years.
We'll, yes we do. That is what the ECS tells us. Have a look at Chapter 3 of the Technical Summary of The Physical Science Basis of the IPCC's AR6 at www.ipcc.ch.
No. I doubt our atmosphere could hold that much water even were the planet at 100C. Eventually, one way or a very unpleasant other, humans will stop burning fossil fuels. Within a few decades, CO2 in the air will start to come down and with it, temperatures. Water vapor decreases and increasing carbonate solubility will both provide some assistance in that direction as well.
