Is there a rule in the manual that allows or disallows counting the amount of event cards left on the table or is that to be left to the house rules?

The same thing for looking at other player's discarded combat cards.

I don't think there is some rule about counting combat cards, but i prefer to not count them as it can slow down (significantly) the game.

The event cards are ok, since you can do it once per turn, without too much hassle.

My house rule is also to not allow players to count cards, mostly because that way they cannot make a decision based on the fact that the game is about to change from Stage I to Stage II or from Stage II to Stage III. If a player knows this, it could affect what they plan to do.

Counting cards is also a way that some players can calculate the odds of drawing one or more of the "The End Draws Near" event cards in Stage III, which is especially important if someone is playing the Aldaris faction (and has chosen the Special Victory Stage I Leadership Card when playing the BW expansion.)

Looking through another person's combat card discard pile, in my opinion, is just bad form--albeit not necessarily against the rules--except when the owner of the pile explicitly allows it.

These kinds of preferences should always be made clear prior to the start of the game so as to avoid potential arguments later during gameplay.