Probability of 64bit Hash Code Collisions

Question

The book Numerical Recipes offers a method to calculate 64bit hash codes in order to reduce the number of collisions.

The algorithm is shown at http://www.javamex.com/tu

Answer 1

Is there a formula to estimate the probability of collisions taking into account the so-called Birthday Paradox?

See: Birthday attack.

Assuming the distribution of hashes is uniform, the probability of a collision for n keys is approximately n²/2⁶⁵.

Is it safe to assume that a collision of a reasonable number of keys (say, less than 10,000 keys) is so improbable so that if 2 hash codes are different we can say that the keys are different without any further checking?

It's only safe when you use a cryptographic hash function. Even if you can tolerate a mistake every 3*10¹¹ times, you may have to consider the possibility that the input is specifically built to create a hash collision, as an attack on your program.