If I manually map and replace the org-id and user-ids when moving the backup from one org to another org, is there any other issues to account for when pushing a backup from one organization account to another organization account?
You have to keep the referential integrity of all ID values, not just the user ID values. This means you'll have to spend time on each object to translate each ID value, and you have to load your records in order (e.g. load Accounts before Contacts, and load Products before Price Book Entries). For a novice, this can be a daunting task, especially if you have a hundred or more objects you're trying to translate. Also, if you want to maintain audit history (created by, created date, modified by, modified date), you also need to have this feature enabled by Support.