Root won't affect imei status, or sim status.
Your sim card slot is carrier locked when the phone is made. It can be unlocked by obtaining a code from the phones branded carrier. Or a code can be purchased online thru a third party.
The imei number is your devices serial number to the network. There is no locking, or unlocking imei numbers. However imei numbers can be blacklisted. This means the phone is possibly lost, or stolen, and not aloud on the network. At&t and T-Mobile share blacklisted imei numbers. The only way to resolve a blacklisted imei is to contact the phones branded carrier and plea your case.