I'm like TXBill, the first three items on your list fit a 240D perfectly.

It's really hard for us to know what your hearing without hearing it ourselves.

As for the battery, put a voltmeter across the battery, it should read about 12 volts. Start the engine and place the voltmeter across the battery, the voltage should go to about 13.5 volts, if it stays at what was measured with engine off, the alternator is the culprit.

Good luck,