Coordination compounds with alkene ligands
Ethylene is a monodentate ligand and there are 4 ligands total: ethylene,  two chlorides, and water.

Regarding hapticity, you can find a great answer here: What does the eta notation mean in the naming of a transition metal complex?

While a chapter can be dedicated to the nature of organometallic bonding, I think it is practical to say that it is the two electrons in the pi-bond that are involved in bonding to the metal center.