Discovery must be complete 30 days before trial, but any discovery motions must be heard 15 days before trial. So while you can serve discovery 60 days before trial (65 days by mail), you cannot enforce that discovery unless the court allows you to have a motion to compel heard on shortened time.
So discovery must be served at least 90 days before the trial date to be enforceable. But that does not account for extensions for mailed discovery or for the meet and confer process. Best to make sure all discovery is served 15 weeks before the trial date.
As to a Bill of Particulars, no response is required, so non-response has no effect.