How to gain access to the entire memory and to the memory of other programs in windows? Is there some function which enables it?

You'd need to make a driver: http://stackoverflow.com/questions/23683707/read-physical-memory-under-windows-8

Also note the need to respect the paging table and segment selectors. Even for a kernel mode driver many pages won't be mapped into its current address space. To reliably read all memory you will have to modify those structures accordingly before acessing, and restore them afterwards to avoid the OS crashing.

Thanks.
PS. How the anti-virus is looking the memory through?

from ring3 you may be sometimes allowed to access virtual memory of different process via
ReadProcessMemory
https://msdn.microsoft.com/en-us/library/windows/desktop/ms680553%28v=vs.85%29.aspx

from ring0 there is
KeStackAttachProcess
https://msdn.microsoft.com/en-us/library/windows/hardware/ff549659%28v=vs.85%29.aspx
after attaching you may use various ring0 procedures beginning at Mm..., you may obtain modules info, you may also parse paging tables from CR3 to last level
You may also register some ring0 callbacks which are hit at CreatProcess, loading module and so on.

To scan physical memory there are some undocumented things like
MmGetPhysicalMemoryRanges
https://msdn.microsoft.com/en-us/library/windows/hardware/ff554435%28v=vs.85%29.aspx
then you may map physical memory pages via MmMapIoSpace to access them by returned virtual memory

CandyMan
\Device\PhysicalMemory is still accessible in the kernel (and even was accessible from user mode in the early XP with no SP). No need to manipulate any hardware dependent structures directly or do anything undocumented. On the other hand it's for very specific purposes, and in most cases one would prefer to look in virtual address spaces.