Is BBS used for generation of keys for any modern cryptosystem? Is there any (current) cryptosystem or digital signature or cryptographic primitive that uses the BBS PRG in order to generate its secret keys?
I don't know of any implementations that use BBS.  I hope no important system is using BBS.  BBS is a poor choice for practical use.  The only benefit it has is that it comes with some security proofs -- but it turns out that those proofs are useless for all practical instantiations of BBS (for realistic parameter settings), so they're pretty much irrelevant in practice.  See Blum Blum Shub vs. AES-CTR or other CSPRNGs for details.