I have a 87 camaro with a E4ME 4bbl. The EGR valve has been removed by the previous owner. I'm now looking to remove the exces hoses to clean up. My question is: Is it ok to remove these and plug the holes? Is there a vacuum the carb really needs? Also, do I really need the front and back brake diaphragms?

Yes, you need the hoses to the front and rear vacuum breaks on the carb. You can run on just the front one, but not without some readjustment to get decent results.

The smog pump system (air pump) and it's related lines are fair game. So are the various hoses to the charcoal canister.

Could you explain to me what these diaphragms really are there for? As far as I educated myself I got that the rear one closes the choke plate fully at start and the front one stops the AV plates from opening but I don't know when and why.

Both of them share one primary function. They both OPEN the choke plate slightly as soon as the engine starts and manifold vacuum is present. This is to prevent from flooding the engine out as soon as it fires up. Front one retracts and opens it a little more quickly- but just bumps it open a little bit. Second one retracts more slowly and then bumps it open a little further.

The front one only also serves a second function- holding the secondary air valves closed. It holds them closed until you go to WOT or close to it (when manifold vacuum drops near zero). Then it extends and lets the secondary air valves open as airflow demands through the carb require it. It acts as a "shock absorber" if you will to prevent them from snapping open and causing a bog when you smack it wide open. This is a critical function on a QJet since it has vacuum operated secondarys with no accelerator pump on the secondary side.

I managed to run the car without the front one(since it doesn't work) and it doesn't bog. Maybe the spring on the secondaries is very stiff and stops them from opening to quickly or too soon.
On the hose to the front diaphragm there is a "T", spliting the hose and I don't know where the other end should go. It was connected to the intake, but is that correct? And what is that thing on the intake? MAF,VAC?

It goes to the air cleaner.