If attached via Line and RCA plugs, both speakers will switch on when signal is played.

You need to use pre-amp out - that is variable line level. Many people do this though obviously the easiest way to use them is with a B&O system.

Will work fine but you need to connect the iMac to the Tape 2 Rec of the Beomaster. You will need some software - I use Toast 9. Best way to improve FM reception is to use an external aerial. A dedicated FM aerial is best but an output from a TV aerial will work better than the internal aerial in all probability.

I have a Musical Fidelity X-CAN V3 - and very nice is it too. Works very well with my Grado RS1s.

There were a fair number of Danish radio makers at one point but the dropping of international trade barriers resulted in all but the strongest going out of business.

The problem with the connection is due to the fact that the Beocenter 4000 was not actually made by B&O but in Japan and hence the odd connections. The Beogram RX had phono plugs to match. I suspect your diagnosis on the stylus is correct. I suggest Soundsmith is the best option but it is rather expensive.

Run a wire from the casing of the DIN plug to a metal part of the beocenter or to a convenient earth point. The Beocenter should have one really but I cannot see one on the manual.

The metal plate will just glue back on - they all fall off because they were originally stuck on with two sided tape which has rotted. I use two pack epoxy. You need to clean all the black goo off the plate and the hinge though first! If the stylus has fallen off, you need a new cartridge and the best place to go is Soundsmith . Not cheap though so

Fantastic cassceiver - basically a Beomaster 2200 - one of the best - and a simplified Beocord 5000 - the only all B&O cassette deck. Unfortunately cassettes are no longer in vogue so tricky to sell. I bought mine for £25 some years ago.

Have you balanced the arm? If set to 0 it should float in the air rather than drop on the record. You need to get it balanced and then if using a MMC4, set the weight to about 1.2g.I attach a guide on how to do this.