There are 2 batteries in a hybrid - the one the can propel the can form 1 mile to maybe 40 miles.

Then there is the lead acid battery which is charged by braking - if the car is run for just short trips the Lead Acid battery will go flat.

OP - what sort of mileage has the car done in 3 weeks? and how many miles will it be driven on any one day? - a series short trips of a mile or so will kill the car battery.

If you make a lot of short trips a Hybrid was not the car to but - a straight forward petrol only car would have been a better buy.

Seems odd to me that if the alternator failed and the battery was discharging there was not a festoon of warning lights. Even my Mother's Mini c.1966 would show a red warning light if battery draw exceeded the dynamo's output.

I've only very rarely driven automatics and most of those were TC types many years ago.

Once the engine stops then you'd lose the manifold vacuum (or on a diesel the vacuum pump) and power to the brakes would fade but there should be enough to stop. Even without any servo assistance there should be SOME braking action. Once stationary, if the electric parking brake will not actuate then selection of P should lock the transmission. I wouldn't expect P to act as a brake on a rolling vehicle and would rxpect selecting it while moving to cause damage.

The OP needs to ask the supplier of his new car some searching questions.