AE86 4age engine not starts crank ok backfires to air intake

[Ryo]

We have done compression test on my friends AE86 4AGE and the compressions are good.
My concers now is why the engine is so hard to start with smaller capacity battery i need really fully charged good battery to start the car than starting a few seconds (mine starts after 3sec or so but mine friends i need to wait a while).
Once the engine starts i need to keep it on gas or the engine stalls. Also it feels like running on 3 cylinders as the car really shakes.
It is heard really noisy valves but when i keep it for a while in this condition and engine gets warmer it just start running on all 4 cylinders without helping it with hitting gas and the idle gets stable as well.
My only idea what this mean is that one piston is dragging on piston rings causing load on the whole engine.
I am thinking about properly flushing whole engine or using little petroleum in each cylinder if it makes a difference.
The engine was reuilded more than a 5 years ago but the car was not moving like 4 years and was parked outside. What i remember previous owner did replace pistons with rings without doing anything with the engine block so i bet there can be trouble.
Other things i noticed: Fuel pump was replaced pressure is minimal according the manual, fuel pulsation damper is missing screw above, all injectors sound is the same (have not cleaned them yet) When i service wire the fuel pump without starting the engine i feel sometimes touching the fuel line vibrations like the flow is not right. No idea if this can have so big impact as the pressure is according min specs and the fuel pressure is not dropping. Any ideas what i can do next?