When I turn off the "fasten seat belts"  sign I get the above message in place of the "passenger signs on" message. Then I will get a random "pilot input" message warnings throughout the remainder of the flight (until I turn on the "fasten seat belts"). This sets off the aural warning, which goes away when I disconnect and reconnect the autopilot.

"No Electronics" is a passenger sign that illuminates to let passengers know when the use of electronic devices in the cabin is prohibited. Many airlines are replacing the "No Smoking" sign with a "No Electronics" sign. There is an option in the setup where you can select whether your aircraft is equipped with a "No Smoking" sign, "No Electronics" sign, or neither. The selector for the sign can be put in the On, Off, or Auto position. The EICAS message you are seeing informs the pilots that the cabin sign is illuminated.

 

When you say "Pilot Input" I assume you are referring to the "Pilot Response" message on the EICAS. It is a warning to see if the pilots are still alert and occurs in cruise if you have not interacted with the aircraft in a while. It is an option that can be turned off in the setup.

 

 

When I turn off the "fasten seat belts" sign I get the above message in place of the "passenger signs on" message.

 

This is an airline option that is explained in the intro manual, and as John described, above.

 

 

 

Then I will get a random "pilot input" message warnings throughout the remainder of the flight (until I turn on the "fasten seat belts"). This sets off the aural warning, which goes away when I disconnect and reconnect the autopilot.

 

Pilot Input is displayed as part of the Crew Alertness Monitor, which is also an airline option.  This is also described in the intro manual.  You don't need to go as far as turning the autopilot off.  Keeping the heading bug aligned with your flight path periodically will suffice.

 

Please read the intro manual.  Compared to the rest of the manuals, it's simple, short, and would save you a ton of confusion and frustration.  You will not regret reading it.