don't deregister it - you'll have to wait 180 days before linking the two accounts again.
If you don't want them to see your Amazon Stored purchases, though, you do need to keep the two account separate and not linked. That way your children will not have the option to log in with the other adult credentials. The majority of us customers tend to recommend two totally separate accounts (not linked) with the second one being used for physical purchases like presents
yes it will - don't delete the account, simply break the link and then use the account not on the Fires to purchase presents/surprised. You won't be able to change the registration of their Kindles/Fires to the second account unless you want to repurchase all the apps, games, books, videos, subscriptions for them on the second account.