when i'm playing single-note runs, i find that the open strings begin to ring. i think mostly the lower) strings to the one that i'm playing. so that it gives a dissonant overtone.
i also find that my fretting-fingers often hit adjacent strings unintentionally.
the obvious solution to both these problems is to very slightly palm-mute, but that also slightly muffles the string that i'm playing.
also, if i'm playing a rhythm part and come to an abrupt stop, my fretting hand will inevitably hit strings and frets like you'd just be picking up the guitar by the neck with the amp on.
so how do you correct this?
keep your picking hand farther from the strings, and try and use the tips of your fingers on your fretting hand
With respect to your fretting fingers hitting adjacent strings, just practice. The more you practice, the tighter and more precise your fretting will become.

With regards to open strings ringing(and if I understand your questions completely, which I may not), I usually find that playing guitar is more than fretting and playing notes, it's controling the sound emitted from the instrument. As with playing some chords, there are ways of muting select strings from ringing with either the picking OR fretting hand while you're playing. When running licks that I want to keep really clean, I usually have the outside edge of the palm of my picking hand muting the majority of the strings that I don't want to ring. I also use my fretting hand from time to time to mute strings depending on the passage being played.
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