Hi, I can't help you with the first question, but for the other two you may find this older answer I wrote interesting on the global scale of these revolutions:

https://www.reddit.com/r/AskHistorians/comments/5jkbjz/is_it_sheer_coincidence_that_so_many_revolutions/dbh0raj/?context=3

I mention two sources there: Bayly's is a broader approach and good newer supplementary read to Hobsbawm; the edited volume is more on the converging revolutions.

I've also written a longer thing on influences on the Latin American wars of independence over here:

https://www.reddit.com/r/AskHistorians/comments/4jy8k8/as_south_american_independence_movements/

Hope this helps!

Peasant revolts, often called jacquerie, did happen in France before 1789.

Hobsbawm is writing within the Marxist tradition. The thrust of Marxist views of peasant revolts is not that they don't exist, but that they cannot cause significant social change. For Marx the peasants are like a "sack of potatoes". They may be a collective, but do not share a class interest that can unite them.

So for Marxists it took the rise of the bourgeoisie in France to create a class that had a unified interest in changing society in order to allow them to further the reproduction of capital.

So in this interpretation the peasants that took to rebellion in 1789 and after acted as the spear of the bourgeois revolution. I'd say that this interpretation isn't universal even among Marxists. Albert Soboul studied the peasant participation intensively from a Marxist view, in mid-20th century, and eventually started calling the French revolution a primarily peasant revolution.

So one answer to your first question would be that, for a Marxist historian, the revolutions were the global resolving of class contradictions that had built up due to capital accumulation under the various older regimes. However this view can be seen as trying to fit events into a Marxist scheme of historical development.