I have the exact same model and had the same issue.
Originally, I took the generic troubleshooting steps (reset SMC, unplug let sit, etc.). Didn't work. I then used isopropyl alcohol to clean both the magsafe adapter pins and the magsafe input on the machine. Ran the test again (multiple times) and no error occurred. This was a temporary solution.
A few weeks later, it occurred again so I opened a case # with Apple and took it into the Apple Store Genius Bar. The machine passed Apple's in-house diagnostics. They swapped out the Magsafe charger with a new one and the issue is yet to re-occur (been ~3 weeks).
I asked them the same question about the battery and they did not give me an answer (they don't "speculate"). I assume, however, that if it's incorrectly charging the battery for many cycles, the battery would be affected.
In short, temporary fix = isopropyl alcohol to clean the pins on adapter itself and in MBP. Actual fix = defective charger/hub, both of which covered under Warranty. Go to Apple for definitive diagnosis and receive either new charger or get machine serviced.
Also: it's completely normal for the adapter to get very hot when connected to the machine and charging.