Hi Pete
Tape deck issues will usually be:
No tape playback - broken belts, see member Dillen (named Martin) for replacement belt kit.
No fast forward but okay rewind and playback - this means the jockey wheel which controls fast forward has sized, it needs relubricating.
I recently fixed both issues on my BC5000, see my post here for details:
http://forum.beoworld.org/forums/t/25412.aspx filed under Beocenter 5000 cassette deck in Workbench.
In addition, I believe your turntable issues can be either 1 of 2 things:
1. there is a small grub screw on the arm used for controlling lift height, its up the back of the arm, check for missing screws or incorrectly adjusted - service manual provides this info and is available on this site
2. I think there is some fluid used to dampen the movement of the tonearm, this may have dried up or leaked out and might need replacing, you can search on this site for that info. Note the Beocenter 7000 7002 and 7007 are essentially the same units in terms of mechanics (save some minor differences in the TT arm) so you can search for problems, most people around here have the 7 series units, not the 5000 such as you and I have.
Hope this helps,
Andrew