Is there any way to compute the distance of a planet from the sun/earth, given its day length? In other word, for a particular planet, is there any relation between its distance from the sun/earth and its day length?
(by day length I mean the time it takes for a planet to fully rotate on its axis)

No. There's no relation.

It's the orbital period (the time it takes for the planet to go round the sun once, or a moon to go around a planet once) that is related to the distance of the planet from the sun (or moon from the planet). That relationship is Kepler's third law of planetary motion.

Thanks James. So by knowing that for example the day length in a planet is 1,000,000 times the day length in the earth, there is almost nothing we could estimate about the position of the planet, right?

No, only that it hardly spins on it's axis. The orbit around the sun is called a year.

So by knowing that for example the day length in a planet is 1,000,000 times the day length in the earth, there is almost nothing we could estimate about the position of the planet, right?

That's right.

They tend to spin in the same direction because of the way the solar system was formed, out of a cloud of gas and dust. The Sun rotates in a particular direction; the planets orbit in the same direction, and also spin in the same direction.

There are a few notable exceptions to the general rule, though. The planet Venus, I think, spins the "wrong way" - opposite to the other planets. And the spin axis of Uranus is titled over by about 89 degrees, so that the planet sort of rolls along its orbit. The theory with these planets is that they were hit by very large objects (the size of planets themselves) when the solar system was still full of debris, and that affected their spin direction.

They tend to spin in the same direction because of the way the solar system was formed, out of a cloud of gas and dust. The Sun rotates in a particular direction; the planets orbit in the same direction, and also spin in the same direction.

There are a few notable exceptions to the general rule, though. The planet Venus, I think, spins the "wrong way" - opposite to the other planets. And the spin axis of Uranus is titled over by about 89 degrees, so that the planet sort of rolls along its orbit. The theory with these planets is that they were hit by very large objects (the size of planets themselves) when the solar system was still full of debris, and that affected their spin direction.

Uranus is actually tilted at almost 98°, which makes its spin technically the "wrong way".

Is there agreement on what defineds the "day length"?

For example, if a planet were keeping the same face turned to the sun is the day infinitely long (ref to time between sun rises) or equal to the year(ref to time between star rises)?

I know that this is "old hat" to astronmers with their siderial and solar days, but without the preceeding adjective, what is the simple term "one day"?

I suspect that on Earth, a "day" is a solar day, but when Nasa etc gives the length of the "day" is it with one universal definiton?

I seem to recall that Venus has two sun rises and two sun sets with each pair having a different time between. - If correct, does Venus have two different "days"?

Also how long is the Uranus day?