And do such counterparts exist? If so, can you use them to replace AmigaOS completely? And if so, it would be an AROS system then, wouldn't be? Would AmigaOS applications work in such environment?
You can get Aros nightly build for 68k amiga (in ISO format; you can use it under Winuae) from here (http://aros.sourceforge.net/nightly.php ) or alternatively you can get Aros Vision (a distribution of Aros 68k, a bit like Amikit, from here (http://www.natami-news.de/html/distribution_download.html ), to study how it is done.
Would AmigaOS applications work in such environment?
Yes, it's possible to run Amiga 68k applications in Aros 68k; Aros 68k uses Zune (an open source clone of MUI), but of course it's possible to also use MUI (for better compatibility)..
You have to use the free Aros 68k roms (get the archive 'amiga-m68k-boot' from http://aros.sourceforge.net/nightly.php ). The roms need at least 2 MB chip ram.
You can go to the official Aros forum (http://aros-exec.org) to seek any help (or you can ask Toni Wilen).