96 Civic EX

I have Honda battery it is about 4 1/2 years old, 100 month battery.

I was getting an oil change and they tested it and said the CCA was testing low.

The car starts ok for now.

But....I think it might be leaking or corroding, my positive terminal keeps developing corrosion around it, I clean it but comes back.

I notice that my car will idle low at times, and when I put on the AC the car will shake, was charged about 2 1/2 years ago and gets cold.

Can a low battery cause this?

No battery light. I do not think the alternator is an issue.