How can I know my FTL drive type? I tried checking several screens but couldn't found the type.
When you look at one of your ships, or in the ship designer, there is a component for your FTL drive. In the designer, it is on the right above your sensors, sub-light engines, and flight computer.
You can look at this to determine your FTL type. You can also look at other empire's ships to determine their FTL type.
I don't have my game in front of me and can't find a full listing of ship components to reference, so I can't say for sure what exactly the component is called for each of the different types, but it should be pretty clear. Look for the key words "warp", "hyper", and "wormhole".
Alternatively, you could just try to move between stars. If there are hyperdrive lanes on the map, then you're using hyperdrive. If you can go anywhere within a large circle that moves with your ship, you're using warp. If there's a large, fixed dotted circle centered at your system, and you can't travel outside of it, then you're using wormholes. There would also be a wormhole station in your starting system.