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The translation speed of a planet orbiting around a star depends on the speed of the rotation of the star?

Nope, sorry. The rotational speed of the star (how fast it spins) has essentially no effect on the orbital speeds of its planets. A planet's orbital speed is determined by the force of gravity. For example, a planet in a circular orbit travels at a continuous speed which exactly counteracts the force of gravity pulling it toward its star.

The speed of a planet in its orbit is determined primarily by two things:
1. how massive the star+planet are: the more massive they are, the more gravity attracts them together, so the faster the planet travels in its orbit; and
2. how far apart they are: the more distant the planet is from the star, the less gravity attracts them together, so the slower the planet travels in its orbit.

The formula to calculate the speed, V, is
V = K * sqrt (M/R)
where
K is a "constant of proportionality" chosen to make the units come out right (miles/hour, km/sec, whatever)
"sqrt" is the "square root function"
M is the sum of the masses of the two objects, and
R is the distance between the two objects.

Does this clarify anything?

Yes, thank you

Enio,

I thought I should expand on what I've written above, which seems to contradict what Grant and "Evil Dr Ganymede" are discussing in Smallest "earth-like" planet found

I was writing about the large effects that are easily measured on a day-to-day basis. They're writing about very, very tiny effects caused by tides. The results of these forces tend to be noticable only after a very, very long time.

Planets cause tides in the stars that they orbit around, just as the stars cause tides in the planets -- like the Sun does on the Earth. These tides cause the shapes of the star and the planet both to bulge slightly toward one another (and on the sides away from one another, too).

If the star rotates more rapidly than the planet orbits around it, then the star's tidal bulge will tend to be ahead of the planet in its orbit and will tend to pull the planet forward. The planet will be very slightly accelerated and its orbit will gradually become larger. (This same effect is happening between the Earth and the moon, for example. As a result, the moon's orbit is expanding at a rate of about 4cm per year. See http://www.pas.rochester.edu/~blackman/ast104/tides.html )

If the star rotates more slowly than the planet orbits around it, then the star's bulge will tend to be behind the planet in its orbit. The bulge will pull back on the planet. The planet will be very slightly decelerated, its orbit will gradually become smaller and, after a long time, the star eventually will eat the planet.

Also, since a planet's orbit is not perfectly circular, these effects will be stronger when the planet is closer to the star and weaker when the planet is farther away.

I won't try to write a formula here that might describe these effects. The effects are extremely complicated
See http://scienceworld.wolfram.com/physics/Tide.html