As confirmed by the MikTeX developer on GitHub a Biber package is not yet available for MikTeX on Linux https://github.com/MiKTeX/miktex-packaging/issues/2
The download page (https://miktex.org/download) states for Linux
Please beware that MiKTeX for Linux is still in an experimental stage.
So if you need a full and stable TeX distribution on Linux for production then you should probably not use MikTeX since it is still experimental. Use the tried and tested TeX live (maybe in vanilla for newest updates - How to install “vanilla” TeXLive on Debian or Ubuntu?) instead. Biber is available there and is kept in sync with biblatex.
If you absolutely must use the experimental MikTeX on Linux and must use Biber, you can get the Binaries from SourceForge: https://sourceforge.net/projects/biblatex-biber/files/biblatex-biber/current/binaries/Linux/ Note that you absolutely need to make sure that the versions of biblatex installed via MikTeX and Biber installed manually are compatible. Remember to manually update Biber after each (semi-)automatic update of biblatex.
To answer the question you posted. When you use BibTeX as backend you change your biblatex style exactly the same way you would when you use Biber. (You still can't use .bst styles, since biblatex is incompatible with them. no matter what backend you use.)
So if with Biber you used \usepackage[backend=biber, natbib, style=authoryear]{biblatex}, with BibTeX it is
\usepackage[backend=bibtex, natbib, style=authoryear]{biblatex}
Note that since BibTeX is considered a legacy backend, some features may not be available with BibTeX. The full set of features is only supported by Biber. That is why you should prefer Biber over BibTeX.
authoryear? – Johannes_B Sep 08 '17 at 05:21