Question 1: How to get a CryEngine license?
Question 2: How much is the language fee for free games? How much is in paid games?
Question 3: Can I play an fps / tps battle game?

1. CRYENGINE 5 is free. Technically pay what you want but its not required.

2. What language fee?

3. Sure.

How can I build the game.

How can I build the game.

Rightclick your .cryproject file in your project folder.

This thread might come in handy
viewtopic.php?f=11&t=66