What I was going to say was that you aren’t connecting your power supply to the battery, you are connecting it to an intelligent charging circuit which should be managing the battery. It shouldn’t matter what the power supply is doing – if it’s enough power, it should work. The charging circuit should smooth out any noise I reckon.
Batteries can simply fail, but heat also deteriorates them. If it’s getting hot, it might well be due to the heat from the computer itself.
What he said. laptops aren’t great homes for batteries, 2 years of reasonable life is doing well in my experience.
EDIT: Oops forgot the question! I’ve had non OEM batteries that were rubbish and OEM batteries that were rubbish. Personally I’d go on good feedback and buy the cheaper option.