In the same way that the gravity of the sun and the moon affect our tides, does the Earth and the moons gravity have any effect on the sun in a similair way?
Planets probably have very little tidal influence on our Sun since its mass is so much greater. But the way planets are positioned around the Sun do pull it in different directions. This changing motion of the Sun may effect or even cause sunspots to form.
Nasa currently use a method called "planet wobble" to identify stars that have large planets in orbit. Basically, they look for a start that moves back-and-forth over the course of observation. Based on the distance it "moves", the can estimate how many planets are in orbit and their size. Have a look here