Hi Laura,
How are you? Fire suppression shop drawings "should" be part of the plumbing set when you file for the building permit. Once they are approved as part of the set, the sub contractor can use those shop drawings to pull a trade permit for installation.
Question is, are you trying to install a fire suppression system separate from the approved building set?
On the timeline question, DoB has a max of 20 days to respond to any discipline of a building permit, if they haven't responded by then, I suggest you contact the reviewer directly via email or phone. Their contact info is included in the Projectdox application.
Feel free to reach out to me directly and I may be able to help you navigate the city system... it looks obscure but the information is mostly there.
Happy Monday everyone,
ile