Updating to the latest Redpine firmware solved my WiFi problems.
For the modem problems, I created a script at /usr/local/bin/resetmodem with the content:
mmcli -m any --reset
service NetworkManager restart
I made it executable: sudo chmod +x /usr/local/bin/resetmodem
Then I execute sudo resetmodem from the terminal. I’m thinking about setting it up as a cronjob and executing it every couple hours.