What are now Docker cpu requirements for running in Linux, say, Ubuntu and Windows?
Is VT-x/AMD-v is enough or VT-d/AMD-Vi is required too?
Does it require MMU virtualization (Intel's Extended Page Tables (EPT) and Unrestricted Mode, and AMD's Nested Page Tables (NPT) and Rapid Virtualization Indexing (RVI)) like Hyper-V?
Would Xeons with VT-x like 53xx, 54xx run both 32-bit and 64-bit docker images, or just 32-bit or none of them in say, Ubuntu?
May be there is some tool to check for compatibility?
Containers aren't virtual machines. VT-x is not required to run a container. Docker require's certain Linux kernel features. If you have a Linux system on a 3.10+ kernel and a x86-64 CPU, you can run Docker 17.09+.
Windows Server containers require Windows Server build 1709, Windows Server 2016 (Core and with Desktop Experience) and Windows 10 Professional and Enterprise (Anniversary Edition) (all 64bit).
If you want to use Hyper-V Containers, which provide more isolation than Windows Server containers, then you will need to meet Hyper-V's virtualisation requirements.