Help needed with engine fan

[speed]

I've recently had a small leak in my engine bay from somewhere around the fan. Now i don't know lot about engines but i've had a look and the main fan attached to the engine is loose. I can rock it forward and back slightly and the fan and pulley will move. Can i tighten this up or do i have a more major problem?

[speed]

From what i have read the fan connects to the water pump, right? I assume there should be no play in the part that the fan screws onto, so do i need a new water pump?