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the bmw's factory amp has the crossovers built in the amp, if you bypass the amp you will need to add a passive crossover (a simple cap....about 2.2mfd-3.3mfd) for the tweeters or you'll destroy them.
you can run the mids full range and it won't hurt them, the alpine will not be as loud as the factory bmw amp is, i would check the availability of a replacement factory amp, but be aware the 5 series amps are coded to the particular car, the 3 series may be the same....i think this started in the mid 90's.

it definately sounds like a preamp problem inside the amp, i've come across this many times.