Help/advice needed - 159 Selespeed, gearbox warning

[Phreys]

Hi folks, I have a dead-ish 159 on my hands. Over the last week I've had a number of warnings and issues hit me that may or may not be related.  Hoping someone out there can help me eliminate the chaff from the wheat.

The car: 159 2.4 JTDm Selespeed, low kms, clear history, no serious issues, until this (wonderful ) week...

Symptoms/history
1. last week: oil warning light. Then the low battery warning. 
--> Plan to resolve: service/oil change, preceded by some mileage to charge the battery (I do far too few kms).

But before I could act on this...

2. Saturday: the passenger side footwells flooded (heavy rain).
--> Plan: re-seal the inner door panels on both passenger side doors; cross fingers; do a hose-test; cross other fingers.

3. Tuesday: rear passenger window stopped working.
--> Plan: new window regulator (I've confirmed the clip holding the window has broken BUT, for now, I've left the regulator motor off and the wiring hanging free.)

3. Wednesday: engine reving high (1100 vs 750-ish) and pulling unusually strongly.
--> Plan: see what happens after service.  Refer to cross fingers, above.

4. Thursday/today:
a. flat battery
--> jump started (negative clip to the body, not the battery)

b. then multiple warnings appeared: after disconnecting the battery cables I returned to a bunch of warnings. Airbag, ABS, ASR, VDC, Hill Hold, in addition to the oil and battery from last week. 
--> I'm hoping these are being triggered by the low battery charge. (incidentally, at this stage the car was almost stalling when the a/c compressor kicked in every 20 seconds or so)

c. then the gearbox warning lit up: this is when I noticed the 'P' indicator was flashing, as well as the odometer. That's also when the "Have gearbox checked" message came up.  The car is now firmly locked (stuck) in Park.
--> I've tried shutting the engine off and jump starting again.  All is Ok for the first minute or two after starting, but once the cables to the other car are removed the Gearbox warning comes up again.  I assume this timing is coincidental, but...?


Questions
So, I'd be VERY grateful for any opinions on these questions...
1.  Are the warnings for Airbag, ABS, ASR, VDC, and Hill Hold all (potentially) triggered by low battery charge ?

2. I assume the gearbox is going into safe mode, most likely because the Engagement Sensor is unhappy.  If so, is it possible the jump start may have triggered this ?

3. Alternately, could the Gearbox warning sensor be triggered in any way by the low oil or low charge ?

4. Or, could leaving the passenger door window regulator unplugged have upset the electrics and, by extension, the sensor ? (clutching at straws, I know  )

Thanks in advance everyone !