1. The latest version of Dynamics AX is Dynamics 365 for Operations. I have no idea what you mean by "independent AX version".
2. Hosting AX 2012 R3 in Azure is supported. Yes, AX 2012 exposes SOAP web services.
3. Not merged. Rebranded.
4. Not at all. CRM and AX are still separate products, they just share a part of their name, some licensing options etc.