A car that’s left to sit for a length of time will often develop a flat battery as things like the clock and security system slowly drain the battery. But this should not happen in just three days.

If there’s absolutely no drain on the battery (as checked by your electrician) then suspicion turns to the battery itself. It may have done this since it was brand-new, but the battery could have a manufacturing flaw or internal damage that means it won’t hold a charge beyond three days. Borrow a different battery and see if the problem goes away.

This needs to be sorted out quickly as a car that you can't be sure is in Park is always a potential to roll away on its own causing who knows what grief and damage. It sounds like there's something amiss with the way the gear selector is talking to the actual transmission, and any resistance in the action of the shifter really shouldn't be there. That said, you do need to have your foot on the brake to select a gear from Park, so maybe you're taking your foot off the brake pedal prematurely.

You're possibly correct that the two issues are related as a car that thinks it's not in Park, will probably not want to allow you to use the walk-away locking mode. But here's the good news: This is absolutely a warranty issue and Isuzu needs to fix it at its cost.

Book the car in to be inspected as soon as possible and, in the meantime, make sure it's parked somewhere from which it can't roll away. Physically chocking a wheel (with a house-brick, a rock or whatever) isn't a bad idea till it's fixed, either.

This is not an uncommon complaint with MU-X owners nor the owners of many other makes and models. It seems as though some Bluetooth systems prefer an Apple phone to an Android and vice-versa. The solution for some owners has been to change their brand of phone, but that seems pretty extreme. Others have resorted to aftermarket Bluetooth systems, but since your car is still brand-new, it doesn't make sense to be changing the head unit.

The first thing to do is contact Isuzu to see if there's been a new download to reflash the head unit and improve the Bluetooth performance. Car makers constantly chase this stuff, and a reflash might suddenly make the thing play the game properly.

You can check whether the problem is phone incompatibility by trying to pair somebody else's phone (of a different type) to see if it works properly with the MU-X's system.