I have a water leak from backside of engine compartment when either not running or steady water release from backside of engine when turned on.

Heater hoses? Run car and pop hood

The classic cause of this is a head gasket leak to the coolant jacket, which will cause quick overheating.

You may see white bubbles in the coolant like dry ice, if you start the car from cold, allow the temp gauge needle to just move off the stop, then remove the radiator cap by grasping it through a large towel spread wide on top. Look then down the radiator neck while the engine runs and warms up.

There is a simple test for combustion gases in the coolant, which your local mechanic can do.

https://www.youtube.com/watch?v=a3J00_e7fyo

After engine has cooled, put water in the radiator if you can, not the overflow bottle.
Antifreeze raining down - sounds like a water pump leak, or other SERIOUS leak, in a rubber hose, etc. You can ruin the engine if it overheats! Guage will not work with no water in the engine. Have reliable mechanic check it ASAP

You should be able to trace the heater hose from the Firewall back to the engine. That is one possibilty. Sometimes depending on how water circulates in an engine, the intake manifold can distribute water and a leaking gasket will let the water out.

There are tools which can be borrowed from an Autoparts store for a returnable deposit. You would want a Radiator pressure tester which will alow you to test the engine when it is cold and force water out of the leak.

The heater core may be leaking or a coolant line near the firewall. The fact that the inside isn't wet doesn't mean it is not a heater core problem, as the plastic catch pan may redirect fluid to the firewall 'weep' hole.

The main thing you will need to do is to minimise the amount of 'excessive' engine fumes being generated in your engine compartment which in turn will 'leak' into your car compartment: 1) Degrease your engine and check for leaking oil gaskets especially around the oil refill area: oil leaks at the back of the engine falling on your hot exhaust pipes and on your engine block will generate lots and lots of 'nasty' smelling fumes! 2) Check that your exhaust pipes joints are well sealed especially the one contained within the engine compartment: taking great precautions, check for the obvious leaks from smoke emitted but you could use soapy water to assist. 3) Check that the lining in your engine compartment are in good condition taking particular attention to the 'Firewall' ones (e.g. the one between the engine compartment and the passenger side compartment). 4) Check for broken heating/cooling air hoses leading into the passenger compartment.
Hope it helps!

leaks in this vicinity are usually from the seals going bad on the water pump. It's next to the PS pump, and is very common to leak there in any vehicle. Look at the pulley for the water pump, do you see streaks on it leading out from the center? This will confirm it. Recommendation: replace your water pump.

Sounds much like a vacuum leak; this would definitely cause rough running and the power brake booster is dependent on engine vacuum.
This should have turned on the 'check engine' light though -

check the soft rubber drain tube inside the engine compartment it hangs down between firewall and engine, squeeze it to let the water out probably cloged. if cloged it backs up water into the passanger compartment and leaks inside car

your heater core is going out on the car...its leaking water into the car