There's already an Android app for Tautulli, hasn't been updated for a while but still works fine - Tautulli Google Play
PIA is a private internet access VPN, it's used to mask your outside IP address to the world which allows you to browse online anonymously. With PIA you are creating a VPN connection through their network so the traffic looks like it's coming out of whatever endpoint server they route you through.
You cannot use PIA to securely connect back to your home network. You need to host your own VPN through hardware like a VPN router or software like LogMeIn Hamachi. The software route is a little easier if you're not comfortable with advanced networking.
If you are using Jacket (with NZB360) remotely either on the same network or outside, you need to
1) open the port used by jackett in your firewall
2) modify ServerConfig.json in the jackett directory, set AllowExternal to true.
Here is a thread with details: https://github.com/Jackett/Jackett/issues/415
After you have made these changes check to make sure you have remote access by accessing jackett remotely through your browser.
That's good, sounds like the computer is reachable then. I would verify that port 8989 is open on the computer to your android device
Use a port scanner like: https://play.google.com/store/apps/details?id=com.twistandroid.portscan
Put in the computer IP and port 8989, is it Open?