My idle is not really stable and my temperature gauge behave weirdly i.e. : show normal temperature but get a sudden drop before returning to its normal position (only at idle)

Do I have problem with my water pump or a belt or something like that?

Sounds like a rusted ground. Clean the ground wires at the fuel rail bolts, and clean both ends of the grounds from cam cover to firewall.

The what in what where?

fuel rail bolt?

There are 2 10mm bolts that attach the fuel rail to the intake manifold. They both have a multitude of ground wire connections on them. Remove the bolts, clean the terminal connectors up and tighten them back down... Don't miss any ground wires when you put it back together...