Strictly an estimate: there are 3-4 generations of humans per century. (I base this on my great-great-grandfather, who died 101 years before I was born.) Let’s use 3 [sup]1[/sup]/[sub]2[/sub] per century for an average.
Mathematically, you have twice as many ancestors for each generation back you go; i.e., your parents are 2 ancestors, your grandparents are 4 ancestors, etc. Summing these for n generations: 2[sup]1[/sup] + 2[sup]2[/sup] + [sup]3[/sup] + … + 2[sup]n[/sup] = 2[sup]n+1[/sup] - 2.
So, going back 2 generations gives 2[sup]2+1[/sup]-2 = 2[sup]3[/sup] - 2 = 8 - 2 = 6.
Going back to New Testement times is 20 full centuries or 70 generations. 2[sup]70+1[/sup] - 2 = 2[sup]71[/sup] - 2 = 2,361,183,241,434,822,606,846. ( 2 sextillion, 361 quintillion, etc.)
There obviosly haven’t been that many humans ever in existance, but there are that many branches in your family tree. There are mostly duplicates at this level, so were all basically inbred if we look back far enough. :D:D
And this was just for the last 2,000 years. Mankind has been around a couple million years, our generations were closer together, and the previous species we evolved from most probably had very close generations too (probably closer).
Once we get back to sea creatures, our generations were probably only a year or two apart. Back to simple multicellular creatures, there were probably a few generations per year. Back to single-celled creatures, there were probably several generations per day.
As to whether we are descended from dinosaurs: unlikely, probably no. Mammals probably descended from shrew-like creatures that co-existed with the dinos. They were too small to be fodder for large carnovores and prolific enough to not be wiped out by those that did eat them. And when whatever event that killed the large dinos happened, the proto-mammals were ready to fill all the evolutionary niches left empty. Birds are most probably the descendants of dinosaurs. (Not the large lumbering ones like triceratops and bracheosaurs, but the two-legged raptors.)