Is it true that the water you drink was someone's urine previously ?

Given enough time yes.  Molecules of water that Julius Caeser or Jesus peed into a river have probably arrived in your drinking water.

Not in that form. Water will hold bodily waste until it evaporates back into a distilled form or there about. Water recycles from usage on land back to evaporated humidity. It then rises to meet with colder air and condense back into water droplets and rain back down to be used again. The stuff that makes uric acid in the water is left behind when the water evaporates back into a pure form of H2O. That's one reason evaporated water doesn't have a taste to it. It doesn't have all the minerals in it that makes it taste like water until it meets the ground and then back into streams, rivers, lakes and wells.

Yes.  In fact, it was, at least once, the urine of a tyrannosaurus rex.  It has been bathwater, drinking water and coolant for an engine.

Some of the molecules will have been in urine.  Animal and human.  Given the number of water molecules on the earth and the relatively limited time living organisms have been on earth the probability that even one millionth of the water available had been used in this way is very small.

You answer your own question. water and urine are not the same thing. Thus the answer is no.

It is high probably that when you drink water some of the H2O molecules in it may have been part of the urine of another human or animal. It may have been part of other body fluids of humans or animals.

That does not make the water not fit to drink.

there are some molecules in there that are very likely to have been in somebody's urine or some animal's urine, sure.  Considering that a glass of water has something like 10^24 molecules (1 followed by 24 zeroes), though, it isn't a real problem.  Still water anyway even if the number were high.  More recycled bird crap in your veggies that recycled urine in your water.

No.  The water that you drink was previously the WATER in someone's urine, the water in Noah's flood, and the water in the iceberg that sank the Titanic.  But water is not urine, so the water that you drink "was" not anyone's urine.

At least it is from the fish in that water.

Yes, it's ex-dinosaur pee.