Well…several things there: I guess you wanted to say 12/24/36 days for the temporal “resolution”, but not 16/30, otherwise you may not be using Sentinel-1 images belonging to the same track
Regarding your questions:
- With SNAP you cannot today reduce atmospheric phase error with an specific operator, but you can always check the literature to understand what are the constrains.
- If you pretend to apply PSI, no filter should be applied.
- spatio-temporal filters worked nicely for Envisat data, but nowadays an entire research field opened with the use of weather models, GNSS, etc… just decide what you want to do. I do not like particularly weather models, but this my personal opinion. Approaches like SBAS reduce the atmospheric noise pretty nicely. I like the approaches which remove the APS based on the data itselft and does not need other auxiliary data.
I hope this helps a bit.
Good luck!