What are the pros and cons of deterministic site-specific password generation from a master pass?
The above scheme does have a very important drawback against schemes that encrypt a password store. If you randomly generate the site  specific passwords then there is no relation to the master password. You would need the complete password store to perform e.g. dictionary attacks to find the master password. This is not true for the deterministic password generator you've described; one single leaked site specific password would enable an attacker to launch an attack on the master password. In the following two paragraphs I'll focus on the security without regard of this observation.

It seems that the scheme above is just an application of a Password Based Key Derivation Scheme (PBKDF), coupled with a deterministic method of mapping the result to a new password in step 5. As long as step 5 only maps to an array of characters in a specific alphabet without loosing entropy, the security of the scheme depends on the PBKDF used. KDF's commonly already include parameters specific to the secret that is to be generated (in this case that would be the site name).

So for the security of the scheme you should simply study security of PBKDF's and - if possible - the security of the specific PBKDF that is being used. Maybe you can compare the scheme against well known variants like PBKDF1, PBKDF2, bcrypt, scrypt or e.g. the proprietary OpenSSL PBKDF.