None of those phrases are used everyday. Still, they don't sound wrong, and I certainly understand what you mean.
I did a couple searches with Google's NGram viewer:
fell/came under suspicion
"Fell under" used to be more used, but "came under" passed it around 1950. Currently, "fell under" is at about %0.00000150, whereas "came under" is at about %0.00000300.
fell/came under investigation
"Came under" has been steadily increasing, and is at about %0.000000800 as of 2000, whereas "fell under" has never hit %0.000000100.
So these phrases are all used, to at least some extent. It appears that the "came under" phrasing is more common, at least in published books, than "fell under", and even more so with 'investigation' than with 'suspicion'.
Always take NGrams with a grain of salt. They only tell you so much.