Alert in in a nutshell - You can't be surprised... Other creatures don't gain advantage on attack rolls as a result of being hidden.
Assasinate - lvl 3 - You have advantage on attack rolls against any creature that hasn't had a turn yet. In addition, any hit you score against a creature "that is surprised" is a critical hit.
"That is surprised" is interesting because it would imply your attacks you have advantage on are those such attacks, which would mean the Alert Feat not only stops auto crits but also the advantage rolls. That might be a stretch. Am I misreading the text? Surprise happens at the start of an encounter only. I don't see it have anything to do with having advantage so maybe not. The advantage might have to do with the assasin being hidden, making an attack in a Psuedo-surprise attack since he is an assasin. They seem relatable but I might be missing something.
Please advise. Thanks in advance!
-JI
You are reading too much into it. Alert prevents advantage from being hidden but the advantage for surprise on the assassin doesn't state it's the effect of being hidden. It would be superfluous if it was. Assassinate is dependent on surprise and alert prevents surprise so no critical from assassinate would take place but the advantage would still work because that's independent of surprise (it depends on initiative order) so the sneak attack is still possible.
Sneak attack would work because of assasinate ability to hava advantage against anyone that didn't make action this turn. If you win initiative.
But, if you try to surprise assassin with this feat and lose the initiative roll, he get's to sneak attack you 