Is it okay if my laptop is always plugged in so that my battery is charged 100%? Must I allow it to drain periodically by unplugging to increase battery life?

Most laptops are either lithium ion or lithium polymer batteries. And they have finite number of charge discharge cycles. A general misconception is that charging your battery all the time while you work will harm it

No. It will not. Once a battery is @100% , the charger port will rout the incoming power directly to the power supply of the laptop bypassing the battery. Analogous to using a laptop without a battery while connected to power source.

Do not drain your battery. It does more harm.

Anyways whatever you do, the average difference in life of similar batteries would be a max of 8–10 months depending on usage.

An important point. Battery life is reduced drastically if it overheats , that is the major culprit. Use an external cooler pad while working