Yes Batu Caves.
I went there three times every week to 'train' before I climbed Mt KK. Back then I was 12 years old btw.
I also climbed Penang Hill for training once. Didn't really do anything else other than that.
And yes I made it to the peak.

Breathing difficulties quite hard to say I think. Some may be very fit but still encounter breathing problems. My parents have climb Mt KK at least 7 times. They haven't had any problems with breathing difficulties before. Can be quite cold though, be sure you are well prepared for the cold weather.

I've had family relatives who went up with my parents previously, some of them were already vomiting non-stop at the hotel at Laban Rata. So they couldn't continue the climb for the 2nd day.
As for me, I did feel a little nausea when I was near the peak but still made it up and down without much problems.