My apologies in advance for not downloading/testing/fixing the game...
I'll try to answer a couple of the questions at least if you're still having issues, but they may not be exactly what you'd like to hear.
First problem- Sounds like a problem with the conditions/actions in your event sheet... if it's a timing problem, try inserting a "wait" action BEFORE issuing the health increase... 0.05 seconds should do :P (Sorry if it's unclear or simply doesn't help)
Never encountered that issue before... Sorry.
Third Problem- Sounds like another condition/action problem... I would suggest moving the play sound action to the key pressed condition... If you're using ammo, you could simply a sub-event with a check ammo variable condition... Or something similar.
Fourth Problem- Well, AI isn't exactly "easy" to work with... And combining those behaviors "can" result in unpredictable results... Time for trial and error I suppose... The new line-of-sight behavior may help, along with AI pathfinding. But again, trial and error.
The main resolution for most of these problems is digging into the event sheet and testing the changes. If any of these work/don't work, let me know.