> When I ran arp -a it reported "No ARP Entries Found".
ARP Table is a fundamental resource in IP networking, so, something must be there. ARP Table isn't updated until you start communicating with adjacent nodes in the network (ie. router, other PCs on same switch, etc). So, if you're reading this web-page, you must have at least the entry of the nearest router or gateway in the ARP Table.
> Under "Settings->Alerts->Printers" there is an entry for printers. I never put in any info for alerts. Should I just get rid of all the entries? What are these alerts doing?
Well, what are the enties in there? Avast can configured to send alert when a virus is detected, so, perhaps at startup it's ping-ing the node hosting the printer. Provide us screen-shot so we don't need to guess.