What is best practice for charging galaxy tablet? Will charging for long periods 24/ 7 damage it? Will leaving my galaxy pro tablet plugged in 24/ 7 cause any damage?
It's true that the underlying technology behind Lithium batteries cannot stand being overcharged (batteries that are overcharged may overheat and explode); however all consumer grade Lithium batteries have a chip that controls the optimal charging strategy and automatically cuts off the current once the battery is full. 

Barring manufacturing defects, yes, it is safe to keep your device charged all the time. Keeping the device in the charger as much as possible is, in fact, the best practice to prolong the battery lifetime.

If you're in situation with heightened risk of having devices with manufacturing defects though, for example if you are running an application development shop that have dozens of continuously plugged devices in a small space, you may want to minimize your risks by switching the charger off when the device are not being used. This is good for saving energy anyway.