Good advice on the fuel pump above. I'll add ...

The original pump was made by Pierburg, since bought by TI Automotive. So if you wanted OE quality without paying for the BMW logo, a Pierburg or TI Automotive one (my replacement said Pierburg on the box, and was stamped TI Automotive on the shell of the pump itself) should get you that.
16-11-6-755-043 fuel pump w/o sender (just the pump = Pierburg 7.22013.57.0)

Given that your current pump has not died yet, you might consider carrying it as a spare just in case you need to use that FCP warranty one day.

Not sure what your 4.4 needs, but on my 2001 3.0i, the OE fuel filter was a Mahle KL96, 13-32-1-709-535. That includes the fuel pressure regulator. I believe some of the filters come with the regulator and some don't.

On the temp sensors, it just sounds like you need to track things down carefully - exactly what sensor is being reported as out of spec - find that and test/replace it will probably be what you need. Sounds tough since you have so many factors in there that are at least a little doubtful.

Good luck.

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2001 X5 3.0i, 203k miles, AT, owned since 2014