can heavy rain and thundering cause a tsunami?

No

they cause floods and sometimes flash floods

earthquakes, volcanoes and lanslides can cause tsunamis

There aren't any recorded, however it is theoretically possible. Winds during a hurricane rise what is called the surf. The winds have such force they push water inland, however, it a consistent rise in water, not just a single wave, therefore it isn't technically classified as a tsunami. Most tsunamis we hear about are caused by thrust earthquakes that occur in the ocean. This is where a slab of the earth's crust is thrusted upward displacing the water above it.

No...tsunami are body waves that travel throughout the entire ocean depth. They cannot be created by weather phenomena.

Tsunami are created by displacement of seawater. They are most often caused by vertical displacement of seafloor along faults. The biggest fault displacements occur along the megathrusts of subduction zones.

Tsunami are also caused by submarine mass wasting, such as the flank collapses of volcanoes (Hawaiian chain has had many), rockfalls (Lituya Bay, AK is biggest tsunami on record), volcanic eruptions, and meteorites (probably create the biggest of all).

Nope. It has to be an earthquake.