UPDATE!

Ok so here's the short version.

Went to KIA Pasig and all they said was it was my transmission and charged me 75k for it. They didn't even check the engine. Forget that, so I went to my trusted mechanic and did the following.

Repairs:
-Engine overhauled due to water seeping in cylinder 3.
-Changed spark plugs and ignition wires
-Changed Oil and oil filter
-Changed gas pump and filter
-changed the TPS
-cleaned/flushed the radiator

Results:
-Car got a bit of HP back while under heavy load, but still not even 70% of it.
-Car runs now even better with ac off, lakas ng hatak.
-Engine is whisper quiet
-AC now colder

New symptoms:
-Idles roughly and surges and stalls when engine is cold
-Sometimes while running, I can feel the steering wheel and brakes become stiff as though its about to stall.
-Wiper stops sometimes while on low.
-Lights in instrument panel gets dim when I turn on the headlights (80/100w)
-Exhaust smells somewhat like raw gas

Best guess:

I also brought the car to a battery store, they checked my charging rate and it's about 13.8-14volts when idle, and about 12.8v when under heavy load (AC, headlights and radio). Under powered alternator or bad battery? I don't have problems starting the car even after 2-3 days of not using it. But it sometimes stalls while running. especially when it surges right before I stop.

I feel that with the engine running great, it now shows problems with my electrical system. I feel that my alternator and battery might be on its way out. And with that it might not be supplying enough current to the computer box, making it go crazy causing the surging and stalling. Would that make any sense?

Question:
-Would changing the alternator (upgrading it to 90amp from 60amp) and battery be a good next step?
-Anything I should look out for should I have my alternator changed?
-Any recommended shops where to get one and to have it installed?