Plesk - What ports need to be opened for all of PSA's services to work behind a firewall?

Generally it depends on what services are running on the server. All the ports which can be used by Plesk/services are listed below:

#20 ftp-data
#21 ftp
#22 ssh
#25 smtp
#53 dns (TCP and UDP)
#80 http
#106 poppassd (for localhost only)
#110 pop3
#113 auth
#143 imap
#443 https
#465 smtps
#990 ftps
#993 imaps
#995 pop3s
#3306 mysql
#5432 postgres
#8443 plesk-https
#9080 tomcat
#5224 (outgoing) plesk-license-update