Ok, the indent you can remove by either placing noindent in front of the line you want to have without it to remove a parindent locally

or

you place a setlengthparindent{0pt} in your preamble to disable parindents globally.

Loading the microtype-package can also help in reducing overfull hboxes

Your code would then look like this:

documentclass[paper=A6]{scrartcl}
usepackage[automark,headsepline=false,footsepline=false]{scrlayer-scrpage}
usepackage[showframe]{geometry}
usepackage[english]{babel}
usepackage{microtype}
begin{document}
newgeometry{left=8mm,right=8mm,top=8mm, bottom=8mm}

noindent[17-20/44][1/6][1-2/2][23-26/50][4-7/12] 5x[16/16][1/1]

sometextsometextsometextsometextsometext sometextsometext

end{document}

Edit

The example given is not exactly fair, since in a regular text you wouldn't have to deal with words of such length (except if you're Welsh or German). You can always insert allowbreak inside words if you want them to be broken without hyphenation:

documentclass[paper=A7]{scrartcl}
usepackage[automark,headsepline=false,footsepline=false]{scrlayer-scrpage}
usepackage[showframe]{geometry}
usepackage[english]{babel}
usepackage{microtype}
usepackage{blindtext}
begin{document}
newgeometry{left=8mm,right=8mm,top=8mm, bottom=8mm}

noindent[17-20/44][1/6]allowbreak [1-2/2][23-26/50]allowbreak [4-allowbreak7allowbreak /12] 5x[16/16][1/1]

blindtext

end{document}