Power adapter green light blinking on - non genuine adapter
A blinking LED is not a signal that the original MagSafe Power Adapter would output, so it's hard to say why it does that, perhaps contact the manufacturer. But it sounds like there's something wrong with the adapter.

It is technically possible that a faulty power supply hurts your battery or even your machine (as in logic board, etc.). I have experienced several MacBooks that have been bricked by 3rd party batteries in my time as an Apple Technician.