Moving notes = moving them from the notebook they are in to a different one.
Local note = this is a legacy thing, where they're not stored on Evernote servers. Evernote moved away from this concept with Evernote 10 so that things are simplified (if the notes are in Evernote, they are in the cloud).
Free plan = You can log in with 2 of any combination of the following devices: Mac, PC, Web browser, iOS or Android.
While you're waiting on Support, I highly recommend this article with answers to a lot of these questions: https://help.evernote.com/hc/en-us/articles/23565231682323-Note-and-notebook-limits-in-Evernote-Free-December-2023