Mavericks 10.9.1. Gmail migration

I migrated using Migration Assistant from MBA running Lion to MBP 13" Retina(Late '13) running Mavericks updated with the update for fixing gmail issues. My Gmail settings migrated. To cut a long story short, after many attempts at trying to remove duplicate emails in multiple Mailboxes, I finally have the following situation:

Inbox shows all Gmail mails

Sent shows all Gmail mails

All Mail shows all Inbox & sent mails again

Then there are SMART MAILBOXES

I.E. ON MY MAC - showing some deleted & recovered messages

and

GMAIL with all its sub Boxes- some empty and some showing mails eg: Important.

Question:

1. Is this normal? Sure does not look so!

2. Can the SMART NAILBOXES especially GMAIL be removed without impacting the main Mailbox?

3. Should these be just left alone as they are only annoying and not really interfering in anything?

Thanks for any guidance.