Does "false imprisonment" means the same as "taking someone hostage"?

Not at all. A hostage is being held for something, usually money but maybe just as a human shield. Now outside Govt context(political prisoner or falsely convicting someone of a crime) false imprisonment could be kidnapping or just tying someone up against their will(don't plan to take them anywhere but could plan to rape them or something).

It can.

No. They are not even related.

among other actions, yes