>>2How is encryption related to "random" numbers
are you seriously asking?
1. encryption keys should be as random as possible, that's why we have CSPRNGs (cryptographically secure pseudorandom number generators)
2. ciphertext should be indistinguishable from random data
3. the very idea of stream cipher (RC4 is the most popular example but it's not very secure) is based around random number generators: key is used as seed, the RNG output is combined (usually by xoring) with plaintext bit by bit.
>>1it seems to be a constant used in some (mostly proprietary) RNGs. I don't know why this one, in a good crypto application each constant is one of the standard NUMS (nothing up my sleeve) numbers used to show that the generator is not backdoored throug some obscure mathematical magic. common NUMS are square roots of low numbers (e.g. SHA1 used sqrt(2), sqrt(3), sqrt(5) and sqrt(10)) or well-known constants like pi.
how does your crypto work btw? is it a stream cipher or a block cipher? is it similar to any popular algorithms?