I write simple fasm PE 32 bit program.
This program load compiled ELF asm code.
And must run ELF code.

How correct load in some place ELF and run in my Fasm PE exe ?

Pseudo code

In theory it is easy reading elf headers - according to them allocates pages with apropriate (read, write, execute) permissions. copy content of file to that pages. then reading elf relocs and aply them. then must be resolved imports to their windows analogs. All sounds simple only in theory.

On practice thou have to know elf format deep detail.
thou have to know what api equvalents in both OS, and how from one parameters set wrap to another.
thou have to know how to allocate memory with permissions.
And moreover all of work would be unusefull if in used part of elf code would be even one syscall.

Contrvers task - using PE in ELF looks more simpler due to (PE - is most documented executable format in world),(PE commonly never uses syscalls).

If your windows supports WSL (Windows Subsystem for Linux), you can run linux binaries natively. There is already WSL 2 in latest windows insiders.