Hi Kami,
If your guitar amp has only one input then you are basically running two separate systems ... one guitar and amp, and one powered keyboard.
If volume is not an issue - you can still choose to run the guitar pedal into the inputs on the keyboard and send the entire mix into the guitar amp. As a rule, guitar amps don't sound great for keyboard, but there are exceptions to every rule too. Try the processor directly into the kb and see if you like the sound. If it's not what you want, then use the amp, but with only one input, the kb will need to have it's own amp if you want more volume.

The guitar amp input has no control over your guitar's pickups. It merely amplifies the output from the pickups.
Headphone jacks are more powerful than standard outputs, and can cause noise and distortion, so I would use the line outs for the best sound.