How to tackle a large undocumented database

The linked answer tackles the problem bottom-up, database first. As your responsibilities encompass the applications and database, I'd be inclined to attack this top-down starting at the application(s).

Focus your attention on understanding the most frequently used features of the application through consultation with the user base. Trace the database interactions of those features through profiling/logging tools so you can identify the key tables and procedures.

This way your early efforts are constrained to the "stuff that matters", rather than wasting time documenting tables and queries that may be rarely or never used. The focus should also bring the Pareto Principle to bare on your bug fixing efforts (so says Microsoft anyway).