Just focussing on gravers and how to use them, that video of DeanDK's is excellent. Watched it again today, for the third or fourth time, and it is clear and easy to understand, and covers everything you need to know to get going. There's no substitute for practice, of course, but I don't think you are shy of getting stuck in. I can only echo what Nickelsilver recommended for reading, but I'll mention how good George Daniels' Watchmaking is too, on this and every other aspect.
Hi all the previous advice is sound, either the balance complete was changed of it had been re staffed at some point, Usually the balance cock is shimmed to increase the endshake. As old Hippy remarked check the balance cock is seated and parallel to the plate and the balance wheel rim is running flat.