[FabHK]

1. yes, generally and ideally the private key is generated pseudo randomly. But at the beginning or for testing, people might have manually picked a private key.

2. the birthday problem basically halves the exponent security wise. The rule of thumb: If you have N possible outcomes, then after around sqrt(N) guesses the probability of a collision approaches 0.5. So, for birthdays, it's 365 outcomes, so with 19 or 20 people your risk of collision already approaches a half. For BTC private keys, there are 2^256 possible, so with 2^128 guesses you'd approach a likely collision. Fortunately, that's still 1e38, so if you check 1e10 per second, you'd still need 1e20 years to get there.