A:Answer Yes - I have/had both phones, and both fit in the OM4. I use the spring mount rather than the magnetic disc that sticks to the back of the phone because the disc interferes with wireless charging. That said, the spring clip is maxed out with either phone - not dangerously so, but enough so you know that a bigger phone definitely would not work.
Software-wise, everything works as it should with either phone.
I also have the Osmo Mobile 3 and used that with the S20. Both are great gimbals, but you will not be disappointed with the OM4!