Hi Des and welcome to Beoworld
1. & 2, Classic examples of problems with the cords which drive the door opening mechanisms. They may be either broken or simply jumped off the pulleys, it also looks like the runners need a clean and re-lube. I'm by no means an expert on these machines - I leave that title to member joyboygolf (Graham) - but replacement parts are still available for the beocenter 9300 which uses the same mechanism by all accounts. Not an easy job to do though according to Graham. I'm sure he will along shortly to offer far better advice than I can.
3. You want a beolink 1000, there are usually dozens for sale on ebay which sell at varying prices depending on condition, version & how well they are listed. Personally I wouldn't dream of getting one of the after market plastic all in one remotes as they are horrible and just won't do your system justic.
4. There are literally hundreds of speakers out there and the choice is yours. Any make of passive speaker will work but if you are planning on sticking to B&O and want a nice compact speaker then you cannot go wrong with a pair of CX100's. If they are of any great age though then the drivers will have suffered from foam rot but this can be fixed fairly easily if you have decent DIY skillls. If not then many are sold having being refoamed or you can still buy replacement drivers from B&O but again not particularly cheap if you are on a tight budget.
Chris.
The use of metaphors should be avoided like the plague. They're like a red rag to a bull to me.