How much time do I have to take a decision about an event

Ok, I've bought the game finally, so I can answer the question myself.

From what I observed, time speed can be changed by the host, but also the players. It then changes it for everyone (note that I tried this only with 2 human players).

Anyone can pause the game. Other players can't unpause the game for the next 30 seconds.

Having negative piety gives you a bonus to technology rate and taxes, which is how you get the tech rate. There is no unmentioned bonus. Ideally you want to keep piety at one end of the spectrum or the other, both have advantages. Piety is not like Piety in crusader kings, where it is all good. Instead it represents the advantages of secularism (tech, church taxes) versus theocracy (morale and stability).

You can see your current modifiers by hovering over the Current Piety label or percentage slider on the Religion tab. Hover over the flag icons on either end of the slider to see the maximum available modifiers.