Web app can connect, apps can't

Here is a list of best practices for stable server operation:

For your particular situation, concentrate on points 4) – 7), + 11)

  1. Put your Plex server inside a private network/home network
  2. Avoid home network “fragmentation”
  3. Use a designated private IP range for your private network
  4. Give the server and your NAS static local IP adresses
  5. Avoid using more than one network adapter in your server machine
  6. Use wired network connections, disable power saving for network adapters
  7. Use a manually configured port forwarding, instead of relying on UPnP
  8. Don’t let hard drives spin down their platters
  9. Don’t rely on Windows to store access credentials to file servers/NAS devices
  10. Configure “DNS rebinding protection” in your router/DNS resolver
  11. Make sure all involved devices have accurate date/time
  12. Always use a “staging” folder for preparing your media files
  13. Don’t point a Plex library to a “naked” drive letter
  14. Stick to the Plex naming conventions
  15. Never mix up media folders, Plex data folder, and the Transcoder temporary folder
  16. Before assigning an email address to a plex.tv account, make sure it’s actually ready to receive mail

See also The Basics of Remote Access Troubleshooting

Please ask for details, if you are unsure about some of the points.