Why are molecular reactions endo- or exo-thermic?
You are thinking it in a pseudo classical way. In those terms, imagine bonds like some kind of springs with some potential energy. During the reaction there can be rupture or formation of springs, changing the potential energy. In consequence, due to energy conservation kinetic energy must change.

A pictorial argument, that may help comparing your view point about collisions and the chemical reaction case, that is not always true, can be go like this: If we think of two balls bonded by an ordinary spring, in the "relaxed" position (that occurs somewhere between max and min elongation) we have the minimum potential energy. This is also true for a diatomic molecule (look some graph of potential energy curve for a diatomic molecule). Imagine that two of this balls bonded by the spring collide in the region of the (ideal, non mass, non perturbed by the collision etc.) spring and cut them out:



If you make this collision the speed of each ball will remain the same due to the spring is mass less. If molecules were like the balls no change in temperature would occurs, because kinetic energy does not change.

The key point is that molecules does not behave like that, spring never cut so: potential energy always is present. So if they where molecules, as products the separation between balls is larger and so the potential energy is greater and the kinetic energy turns to be smaller.

Now, think in the backward reaction, this reaction would be an exothermic reaction.

I am not sure if that is the kind of answer you need. If not or if something is unclear leave a comment.

Edit
I forgot answer that last questions. Yes, the temperature change can be calculated. Normally what is calculated is the enthalpy change, but they can be related trough heat capacity. Of course there are limitations in precision and size of the molecule, but in essence the answer is yes, it can be calculated following the quantum mechanics principles.