What is the probability of getting false positives?

Seems almost certain to me, but my reasoning may well be faulty. Stats were never my forte.

You're effectively running four different 32-bit hash functions on each string. According to Wikipedia for a 32-bit hash you only need about 110,000 hashes to get a 75% chance of a collision.

Thus with 110,000 strings, getting a collision in all four stands at 75%**4, about 30% chance. That's with 110,000 strings. You have "several billion".

With several billion strings you are going to have a very close to 100% chance of a collision on a 32-bit hash function. With four 32-bit hash functions, that's still close to 100% chance of a collision.

Extending this to having 10 effective hash functions, this cannot increase the chance of collisions. Worst case scenario it has no effect. Here I think it does decrease the chance (difficult , but not enough to be useful.