AndreSantos
1. In the Gmail definition of "archived", yes, archived mail (mail with no labels) is migrated to the "Archive" folder in Exchange Online. Otherwise, not sure what specifically you mean by "archived".
2. You should wait until all users are ready to start using their new mailboxes before you change the MX record. Typically this would be after the initial sync has completed for each of the mailboxes involved. Otherwise, they may only have access to their old content on the source side until the initial synchronization completes.
3. As long as the migration batch is in place, it will continue doing scheduled incremental syncs (usually daily). This means any changes from the source will be replicated to the Exchange Online mailbox. After you do cutover the MX record, you'd usually leave the batch around for a few days so that any mail delivered up to the point of the MX cutover can be synchronized to O365 before you delete the batch and disable the sync.
4. After provisioning the mailboxes, you can use Remote PowerShell to connect to Exchange Online. You can then run: Set-Mailbox user@contoso.com -MaxReceiveSize 150MB to increase the maximum message size up to 150MB.