The no-MMU version of Linux has all of those features except that memory-mapped files (mmap) are limited. These features are the same as in MMU Linux: page cache, dynamic I/O buffering, shared memory. No-MMU Linux also supports other modern memory-related features, like tmpfs, futexes. I think it even supoprts io_uring.
That is not how a VMM subsystem works, irrespective of the operating system, be it Linux, or Windows, or a BSD, or z/OS. The list goes on.
Access to a page that is not resident in memory results in a trap (an interrupt), which is handled by the MMU – the CPU has no ability to do it by itself. Which is the whole purpose of the MMU and was a major innovation of BSD 4 (a complete VMM overhaul).
But three out of those four features: page cache, dynamic I/O buffering and shared memory between processes, do not require that kind of VMM subsystem, and memory-mapped files don't require it for some kinds of files.
I've worked on the Linux kernel and at one time understood it's mm intimately (I'm mentioned in kernel/futex/core.c).
I've also worked on uClinux (no-MMU) systems, where the Linux mm behaves differently to produce similar behaviours.
I found most userspace C code and well-known CLI software on Linux and nearly all drivers, networking features, storage, high-performance I/O, graphics, futex, etc run just as well on uClinux without source changes, as long as there's enough memory, with some more required because uClinux suffers from a lot more memory fragmentation due to needing physically-contiguous allocations).
This makes no-MMU Linux a lot more useful and versatile than alternative OSes like Zephyr for similar devices, but the limitations and unpredictable memory fragmentation issues make it a lot less useful than Linux with an MMU, even if you have exactly the same RAM and no security or bug concerns.
I'd always recommend an MMU now, even if it's technically possible for most code to run without one.
The no-MMU version of Linux has all of those features except that memory-mapped files (mmap) are limited. These features are the same as in MMU Linux: page cache, dynamic I/O buffering, shared memory. No-MMU Linux also supports other modern memory-related features, like tmpfs, futexes. I think it even supoprts io_uring.
mmap is supported in no MMU Linux with limitations documented here: https://docs.kernel.org/admin-guide/mm/nommu-mmap.html For example, files in ROM can be mapped read-only.