Before any fixes that you think are "essential", make sure your manager agrees the priorities, in particular new work vs schema fixes, backups, reindexing or DBCCs etc
Only do essential fixes initially - if the system has been working for a few years then it can probably work for a few more weeks (even without PKs)!
If you make changes, and something breaks, then some users might think you don't know what you are doing. You also might get blamed for (schema) problems that come to light subsequently.
Before you get into making schema and other changes (but I see that you have already started), make sure you have a way of tracking the changes, eg use some sort of schema source control system.
Hope that helps