Noctem
Explorer
For your questions: if a player does not have alert then he will be surprised and can't take any action before the surprising enemies. I think that situation clearly works.
No, it in fact doesn't. You said that the moment the monster wants to attack, IE declares intent, you then roll initiative. All the questions are still relevant regardless of if surprise is a factor or not. Why am I rolling initiative if there's no threat or reason to? Oh I'm being attacked? Ok, by who? I don't know who yet? Ok. Well I take the dodge action since I'm in combat! Oh I can't? Why? Because I'm surprised? But why am I surprised if nothing has happened? And also, why am I surprised if the person who is attacking me is slower than me at attacking? etc..
You've got quite a few problems to deal with for such a simple scenario. It only works properly if the monster attacking goes first. Which is a problem in of itself since if you roll initiative you never have a guarantee of that happening. You're also incorrect in how you're applying surprise if it's how you just explained. You are no longer considered surprised after your first turn. If you go first as a wizard and then end your turn, you can absolutely use Shield as a Reaction vs an attack against you after your turn ends. So your statement that someone can't take any action before the surprising enemies is incorrect.
So your question must be about what a PC with alert does if initiative is called and there is not visible sign of a threat. I treat alert as spiderman's spidey sense. Thus the PC with alert knows as soon as initiative is called that something is about to happen but he doesn't necessarily know what. So yes, he can dodge. He can run away as fast as he can. He can cast darkness on the party to help prevent them from being seen. Anything he wants to do. But just because he has alert doesn't mean he knows immediately where the hidden enemy is at.
No, it is not spiderman's spider sense. Not at all. You have bonuses for certain things and you can't be affected a specific condition. A pc with alert can't immediately tell when combat begins or initiative is rolled. They are simply not affected by surprise should there be cause for it to be applied. Your reasoning is completely flawed. You're also mixing your responses. I've never said they would know where the enemy is. However the rules make it clear that unless you're hidden, creatures know where you are within the range of their senses. Attacking makes you lose hidden on a hit or a miss. So Mr. Sniper in his clock tower is immediately revealed when he attacks from hidden to the party. Houserule of course for situations where that doesn't make sense, that's your prerogative as the DM.