You're asking for a lot of information here, nothing that is horribly difficult, but it all takes time to address.
What you might consider is purchasing a t-harness for your vehicle. A t-harness will address your 6-pin harness questions with nice taps so you won't need to cut and splice into the heavy gauge wires.
The priority door is the driver's door. This is an optional feature and may require an extra relay if your Explorer doesn't already have the keyless entry keypad on the driver's door. The "priority" feature means your driver's door only will unlock after the first press of the "unlock" button on the remote. A second press will unlock the remaining doors.
Sites like "the12volt.com" may have a nice wiring pinout for your vehicle describing the wire functions, locations, and colors for the common alarm/remote start connections.
The starter disable will require a relay and, unless you live or travel to areas of high vehicle theft rates, may not be a wise feature for a beginner installer.
The disarm and rearm wires are probably used as discretes to disarm or rearm the add-on alarm/RS when an OEM method is used. You could utilize the keypad on the door to unlock the vehicle and, at the same time, disarm the aftermarket system you are installing.
The big safety things to consider are to be sure you fuse all the power inputs properly so that if you do make a bad connection, the fuses will protect the wiring and critical systems. You also want to make sure you properly install all the safety features such as the hood pin switch, the brake pedal switch, and the park/neutral switch.
-Rod