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Yes. Yes. An unconnected iPhone purchased on apple.com will not unlock. After activating your iPhone, it will remain unlocked. You can use it with any network offering iPhone service. Only an AT&T Installment Plan is allowed to unlock your iPhone. It will remain locked to AT&T, and it will only be able to work on AT&T networks for the terms of your Installment plan agreement.
Each iPhone comes with a one-year limited warranty that covers hardware repairs and 90 days of free technical support. AppleCare+ and AppleCare+ With Theft and Loss increase that coverage and offer additional features like 24/7 priority tech support and accidental damages protection.
AppleCare+in the United States requires AppleCare Service Company, Inc. to perform obligations.

AppleCare+in the United States requires AppleCare Service Company, Inc. to perform obligations.
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You can receive the AT&T Special Carrier Deal if you are an existing customer and you meet all eligibility requirements.

iPhone 13 Pro Max review.
Express Replacement Service does not apply to screen replacements or backglass damage service fees.
iPhone 13 Pro Max review.

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AppleCare+ offers accidental damage protection for up to two incidents every twelve months.
Yes. Yes. An unconnected iPhone purchased on apple.com will not unlock. After activating your iPhone, it will remain unlocked. You can use it with any network offering iPhone service. Only an AT&T Installment Plan is allowed to unlock your iPhone. It will remain locked to AT&T, and it will only be able to work on AT&T networks for the terms of your Installment plan agreement.