So I bought the ring from signed pieces

now, I have MORE questions about what to do with it once I receive it. I want to take it to tiffany''s and get it polished and authenticated (if they will do that for free, do they?) and I am wondering if I should also get it appraised there. The ring comes with a retail replacement value paper already, but it is from 2002 so I am wondering if the value will have changed. I have not extensively researched insurance options either, but do I need an independent appraisal or will the tiffany one work? I don''t have a huge budget for an appraisal, especially since I only paid $2000 for the ring in the first place, but I do want to make sure that if something happens I will be able to replace it with an equally valuable diamond so I want to do things right. I want a policy that covers anything from damage to mysterious loss, as my girlfriend is not careless but most definitely clumsy.
Also, i haven''t heard back from signed pieces about sizing... do they do it? otherwise I will do that at tiffany''s as well.
so hopefully that is enough questions for you. thanks again to everyone for their help. i feel like i never run out of questions (this is a complicated process!) but now that I have the ring I''m hoping it will all be downhill from here.