Will my lenovo y50 battery get damaged if i keep it plugged in all the time?

No. Modern batteries will look after themselves. You should let it run right down and then charge it fully once a month to keep it healthy but other than that you can use it as best suits you without worrying about it.

Yes. When fully charged, unplug, run on battery till almost empty, plug in again. Leaving it plugged in permanently shortens the battery life.

No. As "Duncan" said, modern batteries will look after themselves