calculating probability and odds for flush draws

[AnotherAddict]

Here are some questions about calculating probability of flush draws.

It is my understanding that in order to calculate the probability of the card you need to complete the hand (P), you divide the number of card unseen (X), by the number of outs you have (Y). Example: 4 card flush draw on the flop, there are 47 cards unseen, there are 9 cards that can help you complete the flush. Therefore, the formula is P=X/Y.
Is that correct?

I have read that when you have a 4 card flush draw on the turn card the probability and odds of completing the flush
Odds are: (47/9)= 5.22 to 1
Probability is: (9/47)= roughly 19.1%
Is that correct?

On the River, Odds are: (46/9)= 5.11 to 1
Probability is: (9/46)= roughly 19.56%

Now, if you have the 4 card flush on the flop, are the probability and odds of getting a flush by the river the roughly 19.56% and 5.11 to 1 ?
Is that correct?

Therefore you must have greater than roughly 5.11 to 1 pot odds in order for it to be a positive expectation and for you to continue profitably.
Is that correct?

I have read that you have a 3 card flush, in order for you to get a runner runner flush on the river, it is a 1 in 25 to complete the flush.

To calculate that it would be (10/47)*(9/46)= roughly 4.1% chance or 24 to 1 odds of completing the flush. Is that correct?

Finally, when is it proper to calculate the number of cards unseen (X) minus the number of cards that will complete your hand (Y), devided by the number of cards that will complete your hand (Y)?
The formula of ((X-Y)/Y). Example, you have a 4 card flush and there are 47 cards unseen, 38 of them will not complete your flush, 9 will. Therefore, it would be ((47-9)/9)= 4.22 to 1 odds.