Hi Enrico,
Yes, Nasm should do fine assembling a program for 8088/8086 (not much difference from a programmer's viewpoint). If you add "cpu 8086" at the top of your source, Nasm will complain if you try to use an instruction not available on that CPU. You'll probably want to add "bits 16", just for clarity - Nasm will default to 16 bits in "-f bin" or "-f obj" anyway. Obviously, the "-f elf" or "-f win32" output formats wouldn't be suitable for 8088!
To *run* such a beast under Linux (or link it, if you need a linker, or trace it), you'll need to do it in an emulator, I think. Dosemu provides a pretty good, but imperfect, emulation of a 16-bit machine. If you're doing graphics, dosemu is not-so-good. Other emulators *may* do better (I doubt it)...
There's a guy who posts to news:comp.lang.asm.x86 who writes stuff for a real 8086 still, as a hobby. (we have "fun" in different ways!) Maybe get some advice there - maybe he'd even test your masterpiece on real hardware for you.
Don't worry about English - the CPU doesn't speak English! :)
Best,
Frank