It seems to be taking a lot longer to process my court paperwork in Massachusetts and/or to get in touch with staff.  Is there a reason for that?

There is a trial court order that at least until April 5, 2021, that the court staff offices have no more than 50% working in a court department or office at any time.  That has had a drastic reduction in how quickly court paperwork is processed and the availability at some courts of speaking to staff.

During COVID-19 can I avoid going to court directly to file paperwork and is there a way to talk to staff other than by phone?                                  

There is what is called “Virtual Registries” for Probate and Family Court in most counties.  You want to look at the particular registry to see how you enter it, but in general it is called a “Virtual Registry”; which uses zoom to use the video conference where you can connect business directly with registry personnel.  You can go to the Registry of Probate for that court and find the zoom link in order to contact the staff person directly through zoom.