A few questions about two X5s

[sv1cec]

God darn, I love the X5, but this car is complicated!!!

OK, here we go. We have two X5s in the family now, mine, which is a 3.0 diesel, 2005 car and our son's which is also a 3.0 diesel 2004 one.

Problem No1: On the transfer case, the actuator resistor has somehow lost its "connector" part, in other words, the part in which the cable clicks in to secure it on the resistor. I have to assume that a mechanic, somewhere, somehow, broke that connector part and just put the cable on the two protruding copper pins. That connection however was intermittent and produced some errors. Problem temporarily fixed, by securing the cable to the resistor with some electric tape, but that's hardly a permanent fix.

My question is about the procedure of replacing the resistor with a new one. I know BMW sells a "resistor set" (part No 27107557345), which from reading the net, is supposed to be a set of resistors. Now, how do you select which one to use on the car?

What a local independent shop did, was to take of the resistor from an new actuator motor they had in the parts stock and give it to me. We plan to change the damaged one with the new one, but how can I tell if the new one is OK for my car? And yes, I know that the new resistor should be coded in the car, after it is changed, but would any resistor do or should I select one from the set? If yes, what's the criterion?

Problem No2: That occured on our son's X5 but it relates to mine too. He got the 4X4 light on. I checked with INPA and there was a 55C4 error shown. We took it to an independent shop, where they diagnosed a steering angle sensor problem. They erased the error and they did reset the steering angle (turn the wheel all the way to the left, then all the way to the right) and they told us that the light may come on again (it did) and that he should first have the car aligned properly and then see if the sensor needs to be changed. So he plans to take his car in for an alignment job today.

On my X5, the steering wheel is not totally centered, when driving straight, it is a little turned to the left. The car drives fine, but the wheel is slightly turned from the dead-center position. They told my son, that this is also something that can affect the steering angle sensor. So my question is this:

Should I have my X5 aligned too, just because the steering wheel is slightly off center? Does that affect the steering angle sensor too? Mind you, I haven't seen any warning lights in my car.

Problem No3: On my X5, it is impossible to fill the tank up at full speed. Whenever I visit a gas station, I have to babysit the nozzle, using only the slower setting, sometimes even slower than slower setting, to fill it up. It's not the pump, it's not the way I insert the nozzle into the filling opening, it happens in every station. So what could that be? Is this something that requires the tank to be removed to fix it?

Problem No4: On my X5, while I had it in the local independent shop for some new suspension parts, we run a check and the electrician said that the electric fan is not working. The car is not overheating (never has), its antifreeze tank is full and everything seems to be fine. How can I test the fan? In other words, when is the electric fan supposed to kick in, in addition to the mechanical fan driven by the engine?

Well, I guess that's it. As always, any help will be deeply appreciated.