»Morpheus believing in Neo too much in M1?«

Alright, my main question that bugs me about the first film (and ONLY question) is all about the stuff before Neo was freed from the Matrix.

How Morpheus can see that Neo is The One....how did he know? How did he know that Neo would not have fallen off the ledge when escaping from the Agents? And why the HECK did Morpheus say, "You are The One, Neo" over the phone that Morpheus knew was tapped?? Also, the removal of the bug scene. Wouldn't the agents know that it was removed and go off to Hotel Lafayette to try and kill Morpheus and company?

Questions like this surround the first Matrix movie:
Agents can take over every body. So why didn't they take over the police men, who wanted to arrest Trinity (the first scenes)?

I was kinda given the impression that the cops were getting killed as the Feds arrived. ("Lieutenant, your men are already dead.")

I'm pretty sure that the agents couldn't have taken over any of the other cop bodies after that. Agent Brown (I believe that was the one tailing Trinity in the beginning) had to take a chance by leaping over to try and kill her. The agent knew that there wasn't another person to take over on that roof. So he leaped in front of the cops. I think the cops would've been more stunned had they seen evidence of an Agent taking over a cop's body.

yah, the reason they didn't take them over is because they were already dead.

I see that this is probably the only plot hole in M1 that cannot be solved. For example, people wonder why Neo didn't hit Morpheus with the gatling gun (Neo had his mind loaded with how to use the gatling gun so naturally he'd be able to control the gun to hit the right places) or how Morpheus got up after that (freed his mind of course in a less severe version of how Neo was raised from the dead). But this one seems to be the most unanswerable.

My question only pertains to the actions of Morpheus and not the agents.

I know why the agents kept Neo around and didn't take over his body: they need him to get to Morpheus and Agent Smith wants the access codes to Zion. However, when the tracer was removed, the Agents lost track of Neo and company and then Neo was freed from The Matrix.