...why did Neo not simply fly Trinity to the nearest telephone exit point instead of waiting for her to die on the rooftop?

There are a few reasons.

1) Not really enough time for all that. Even though Neo could get there super fast, there is still the time delay in making the call and getting her out. She would have died.

2) They wanted to have a little dramatic moment. Thats easier to do if both characters are just sitting there rather than being replaced by CGI that looks horrible. Oh, wait...

3) Inside the Matrix Neo is apparently the worlds finest surgeon and was able to remove the bullet AND restart her heart with only his HAND. Cause that makes sense.

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Bwwaahahahahahahaa!!!!!

Don't be silly. There is no heart.

Well now, that's tricky. Since it's in the matrix, nothing is real, so Neo could only revive her mind. But he did so by saving her 'physically'. Confusing.

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This is where the Matrix myth is revealed as sci-fi based and therefore not making much sense. That's what happens when you don't know when to stop and end up delving too far from where you can go. I'm referring to the WBs making sequels in the likely case that that last sentence didn't make a bit of sense.

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If you want to get into the 'there is no heart' thing then all of the movies are fucked. As in, why do they need to keep putting pretend bullets into their pretend guns.

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Do we even see them load there guns?

and as Morpheus said "The system is build on rules" that they can bend and Neo can break so for Neo its not longer a case of There is no heart and since he was just at the Source he may have been able to effect Trin in the Real World

Also i doubt Neo knows the location of the nearest phone in the Core Network

Why do they have to put imaginary bullets in their imaginary guns? Well Apollo440 said it "The matrix is built on rules". They can only control the abilities of themselves in the matrix, not the things within them, because those objects are under rules. They might be fake, but they're programmed to work as though they're the real thing. Being the one, Neo is really the only one who can alter the matrix to his will, and even his abilities are somewhat limited. Sure the operators could help out, but they can only place items within the matrix they can't alter how they work. Perhaps in their own programs that they create for training, but not within the matrix itself.

And how can neo start Trinity's heart and just stick his hand in and out of there like nothing? He's the one, his mind is more free and can see past some of the most obvious barriers. Barriers of the "flesh". And he's not really affecting her physically, he's just correcting the code of her damaged avatar. Fixing her avatar's condition, will fix how her mind views her condition, thus saving her mind and in the end saving her.

Morpheus: "The body cannot live without the mind." "Your mind makes it real"

I don't pretend to be head guru on this stuff, this is just my interpretation.

Neo didn't fly trinity to the nearest telephone because in the real world he kept having dreams about Trinity falling from a 360ft building. (WHY DID SHE JUMP!!!!! I MEAN C'MON EVEN THE MOST LEAST INTELLIGENT PERSON IN THE WORLD WUNT EVEN DARE JUMP!!!!!!). Neo realised that he had to end his nightmares in the Matrix, which meant saving Trinity in the Matrix aswell.

So even though she knows that she can't fight the two Agents that are shooting at her, and having experience at jumping out of/off of buildings and knowing that theres a chance the person she loves can catch her, i would jump, you'd probably last longer.

also it was the 69th floor