Box 1: No - Most services go to private preview then public preview before being released to general availability. The private preview is only available to certain Azure customers for evaluation purposes.
Box 2: Yes - Public Preview means that the service is in public beta and can be tried out by anyone with an Azure subscription. Services in public preview are often offered at a discount price. Public previews are excluded from SLAs and in some cases, no support is offered.
Box 3: No - An Azure service in general availability is available to all Azure customers, not just a subset of the customers. Reference: https://azure-overview.com/Home/Faq
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