Recently purchased an E53. Have questions!

[SineDeviance]

EDIT: Added a couple new curiosities, they're at the top.

Hi all! First-time poster.

Last month I purchased a 2002 X5 3.0i that just rolled over 200,000 miles (LP38804.) After buying, I replaced a dead alternator and installed new tires on all four corners. I've put about 2,000 miles on it so far. This is my first BMW and I love it! I'll toss up some photos further down. But like any 14-year-old luxury car, it does have a couple of minor quirks. Any fixes, I can probably perform on my own - I'm mechanically-inclined, have a BAFX 34t5 Bluetooth OBDII scanner, and I am going to order a K-Line cable very soon.

Aftermarket Audio:

I have a single-DIN Pioneer DEH-X4800BT laying around from my last car. It's less than a year old and is quite a nice unit. My questions...

1. Can I ditch the Business CD player and replace it with this unit while keeping the MID where it is?
2. Do I need to rewire anything manually, or do adapters exist to separate audio control from the MID?
2. Do adapters for relocating the MID exist if I decide it's easier to go with a regular bezel/pocket kit?
3. What do we do about steering wheel controls?

My X5 Doesn't Go To Sleep:

As it says on the tin, mine does not seem to go to sleep after 16 minutes like most do! I've confirmed with the 12v outlet next to the ashtray; mine never turns off. I've also noticed that the Park light is still on hours after I've locked the vehicle. I've read on various forums that this is normal for some models?

Key Memory:

This has become the bane of my existence! The key fobs/remotes seem to be programmed to the previous owner's seat positions and no amount of trying steps I find on the internet seems to help with programming in my own settings. I'd even be fine with disabling the feature entirely at this point!

1. Is there any way to achieve this without special tools or paying a stealership?
2. Barring that, can I do it manually via K-Line with INPA/NCS?

Transmission:

As far as I can tell, mine has the A5S390R. Sometimes, the transmission exhibits hard up-shifts even with fairly restrained driving. Going from start to stop will kick like a mule about every 10th or 15th time. This also occurs at random gear shifts seemingly through the entire range; it's not always 1-2, or when I go from stop to start. Transmission temp seems to have no bearing on hard shifting.

More worrying - when I floor the pedal on the highway, it will very rarely rev up past redline and hold it for about a second before shifting. This has happened a few times since I've owned the car.

I've Googled these problems extensively but nothing concrete has presented itself.

1. People say there is an EGS firmware update. Could that solve the problem?
2. Service history shows no transmission service; could it just be old fluid/filter causing these problems?
3. Would I be taking a risk by draining it and replacing the fluid/filter at this point?

Rear Camber:

The rear wheels sometimes look as if they have excessive camber after I drive it. But, sometimes it looks okay. The tires are definitely going to wear on the inside faster.

Upper control arms?

Rain Sensor:

From what I can gather from the VIN decoder this vehicle is equipped with the rain sensor (option S521.) However, it does not seem to work. When I flick the wiper stalk up to Position 1 it only gives intermittent interval whether it's raining or not. The adjustment knob also does not seem to have any effect on the interval.

Any way I can diag this? My wiper stalk looks like this:


Headlight Washer Pump:

Unfortunately, mine is out. Anyone know the manufacturer part number for this? AutoZone and Advance don't even know it exists, and I don't want to pay BMW $150+ for a pump that should rightly cost $25 at most.

Rust Spots:

The hood has these odd sections where paint seems to be missing in the body gap on both sides! Rust has started forming there.

1. Is this common?
2. Is there a cheapish way I can fix this?



If anyone has any input into these questions I'd really appreciate the insight! And if you've made it this far, thanks for reading

Photos!
Pre-buy:








First cleaning:




Checking for old fault codes (none) and logging live data: