MacBook Pro Retina 2015 heating up

The fact that your computer shuts down at 50% remaining charge and also that your MagSafe LED remains orange makes me think that either the replacement battery isn't an official Apple part, that it is defective/DOA, or that your logic boards SMC is corrupted and needs to be reset.

If the battery is indeed new and Apple original than proceed with an SMC reset:

http://support.apple.com/kb/ht3964

This will tell the SMC chip to reset all power states and reboot so that it forgets the battery and MagSafe adapter momentarily and then rediscovers them.

Hope that helps

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.