I think I read in the core rules that ambush is a character trigger effect. If so can ambush be canceled using cards like Alannys greyjoy, bloodrider, maester murenmure etc. if I can be canceled what happens, do I still have to pay the influence, do I lose the character I was trying to summon etc?

Ambush cannot be canceled. Yes, it is a triggered "Any Phase" effect, but the FAQ states (in 4.14) that keywords with a point of initiation like Ambush cannot be canceled.

For general knowledge: cancels come between initiating and resolving an effect. So the cost is always paid (since it's part of initiation).

If Ambush could be canceled (as doulos says, it cannot because keywords cannot be canceled), the influence would remain knelt (because that's the cost) that happens, but the card would not enter play, thus remaining in your hand (because that's the effect, which doesn't happen).