Is SF able to read/write VFP 9.0 file format (hopefully natively)?
Yes, we are doing this on our medical system as we upgrade and convert everything over a piece at at time. We use the VFPOLEDB provider....I will tell you that version 9 works better than version 8 as far as the OLEDB driver is concerned. Even if you are talking to VFP 8 data you are better off using the VFP 9 OLEDB provider.
What does each client's machine need to have to run SF app accessing VFP 9.0 Data files?
Other than the StrataFrame assemblies, you just need to distribute the VFPOLEDB version 9 DLL (and register it).
Has anyone made connections to MOM's data files?
I have never heard of MOM before....but VFP data is VFP data regardless of the app 
as far as the connection and communication is concerned.