Problem 1:
Most likely (but not definitely) the SWPS. Mine did exactly what yours did for quite a while before it finally erred enough to start throwing C1287/1288 codes.
What's happening now, is yours is erring just enough to falsely engage AH, but not enough to toss a code and deactivate the system. It will probably get worse, and when it does, it will throw codes, but unfortunately it is a guessing game as to what sensor until then.
Problem 2 has numerous possibilities, and intermittent no-cranks can be frustrating to troubleshoot. Here is what I did...
Remove the pass side floor mat and access panel. Located just above the BCM (big silver box), you will find the Theft-Deterrent Relay (TDR). This relay is where everything in the starting circuit comes together and if you have a voltmeter, keep it there on the pass flloor, because you need to check things mainly when the problem is occurring. If the car starts, there is no problem, and a meter can't help. You have to be lucky to catch it when it won't crank. Also examine the relay itself, I've seen cases where corrosion set in and connections burned/melted.
There are 4 wires connected to this relay:
-A thick red wire, which is a direct feed from + battery. It does go through a 50a fuse, but it is obviously not blown given an intermittent condition.
-A yellow coil wire, which will have +12v (during an attempted crank) assuming clutch pedal switch is made, and ignition switch contact is made.
-A yellow/black striped coil wire. This comes from the BCM, and this wire is normally nothing, until the VATS (key pellet) system is satisfied, the BCM will then switch this wire to ground (-12v),which with +12v on the yellow coil wire, will combine to energize the TDR.
-A purple wire. This is the output wire that runs directly to the starter solenoid. Simply put, if you find +12v on that purple wire during an attempted crank, but the starter isn't cranking, it's the starter/solenoid that is bad.
This is the first wire to check when the problem is happening. If it gets voltage when trying to crank, the TDR is energizing and everything else upstream is working properly. If nothing, then you can start backtracking, depending on which wire isn't doing what it's supposed to.
It took me a long time to have the car "not start" while I happened to have the meter in the car, and this is how I determined when my starter went bad.
Hope that helps.
