Is it true that large Water Dams and artificial water reservoirs can trigger earthquakes ?

Yes. Large dam can trigger earthquake although these earthquakes are typically quite small. Hoover dam is a commonly cited example of a dam that produced earthquakes. I am not exactly sure on the mechanism that produces the earthquakes but the earthquakes are probably caused by the enormous weight of water in the reservoir as the earth around the reservoir adjusts to the new weight. The earthquakes are too small and shallow for water seapage to be a primary cause.

No. Surface water of any kind has no relation to tectonic plate movement. That occurs many miles beneath due to other natural processes within the earth.

Reservoirs have been known to cause small earthquakes.

It is true that the building of dams and the redirection of rivers have slightly altered the wobble of the Earth.

No, I don't think that's true. Water can't move giant plates. The only think I can think of is that water could lubricate the boundary and cause the tension to give a little. Plates are constantly applying pressure on eachother and every so often, they move, causing an earthquake. The water goes into the soil, where it is stored in an aquifer and carried away... the place of high tension between plates is much deeper than this.