There are so many problems here.
What you need to do is go back to basicis IMO. That means formal obedience training.
I agree with gryphon in that e-collars can be a great tool for training a dog BUT, only when you know how to train a dog to start with.
No offense but many of the problems you describe I believe are due to your not knowing how to train this type of dog, or deal with these types of problems, correct?
If you then resort to using a collar as a substitute then I reckon you're starting down the road to disaster.
If you have problems with 'hard mouth' now, wait till you intorduce the collar.
The dog is a bit willful right?
He'll bite that bloody rabbit that bites him - have no doubt about that.
NO no no.
I have no objections to collars at all (in fact I use one occasionally to train my own dogs) but this behaviour wont be solved by an e-collar, at least not by you using one with this dog.
Mark my words you'll only make things far worse if you start using an e-collar on this dog.

These are not definitive answers, just suggestions.
There's no absolute right or wrong, just whatever works, BUT, these problems will take thinking from you. So THINK!

First of all - the coming in/running past problem.
Find OR CREATE a place where the dog cannot physically get past you.
I have made boards whcih stick into the ground that I can place so the dog can;'t get past.
Use fences (stand in a gate way). With pups use a hall way.
YOU are the engineer of your dog's success.
YOU have to create a physical situation whereby your dog can't get past.

Sitting away from you to keep the item.
Dont be in a hurry to take it from the dog but when you do make sure the dog knows it's yours.
Start with holding it yourself before giving it to the dog.
If he jumps the give him an open handed whack on the nose.
He must learn that what is in your hand is yours & he cannot take when it suits him.
Now, the sitting. Start without a dummy. Get him to come right in close to you to sit.
How, offer a treat at crotch level. he only get's it when he comes & sits close enough.
As he get's better start moving back.
I can tell my dogs to sit, move back, & have them shuffle toward me without taking their bum off the gound. In time the dog will leanr to come in close to sit.
Next - giving it up.
Ok, he's possessive. He wants to keep it. Fine.
Find something he wants more. What? - FOOD.
Food is a BIG talker.
Yes there comes a time were you dont want to dog dependent on receiving treats but for now give it a try. Dont worry if he drops the item as long as he lets go to receive his reward.
If he starts dropping on delivery it's an easy fix to then get any dog to hold.
This one would be as easy as pie to get to hold. he's already shown you he will.
With the rabbit I'd sit him down, put ahand under his mouth, then wave a piece of cooked sausage under his nose (in your fist so he cant grab at it). When he drops the rabbit praise him & let him have the food. He'll soon get the idea.

The chasing I'll go into a bit later. That's a whole nutha ball game.