You're right that the trees will eventually grow back and replace that carbon (presuming they do not burn again), but it takes many decades. Am I misunderstanding your question?
Depends on the tree. Younger trees capture carbon faster.
Yes, this is true. For instance, the periodic annual increment in a western Oregon douglas fir forest peaks around forty years, and if each year you average the annual growth of all preceding years, the mean annual increment peaks somewhere between 60 and 80 years depending on site class. I only mean to suggest that regrowing a 40 year old stand takes 40 years.
Trees won't necessarily grow back. In a lot of cases native forest species are pushed out by non-native grasses. And some of the non-native grasses like to catch fire.