The paleocene–eocene thermal maximum makes for interesting related reading. https://en.wikipedia.org/wiki/Paleocene%E2%80%93Eocene_therm...
For example was there as much methane trapped in the arctics during the last time CO2 was high?
Does the rate of the increase of CO2 and temperature have an effect? Because it's currently getting hotter far faster (absurdly so) than any other period we have records for.
Yes. But stars like ours burn brighter as they move through their lifetimes, and the Sun is a bit brighter now than it was back when we had higher CO2 levels. That's why a runaway GHG didn't happen back then, but is basically guaranteed to happen within a billion years.
Also, I see a lot of things presented as facts in your comment, you seem to have convinced yourself quite thoroughly.