I don't know this particular drill, but the advice that often crops up on here is to take the old belt with you to your local motor factors and they should be able to find a new replacement to suit, off the shelf - and often at a lower price than from the drill manufacturer.
If the chuck (and it's adaptor??) are slipping out of the taper in the quill, then the first thing is to check that both the tapers (male and female) are PERFECTLY clean - even just a small piece of metal swarf can affect the fit. Cleaning the male taper is easy enough, but it's usually a bit of a faddle to clean the female - I use a bit of tissue wrapped around my little finger then dampened with a SMALL drop of acetone and wiggle it all the way round and round and up into the top of the quill.
If that doesn't stop the problem, are you sure the "tang" (used for removing the chuck and adaptor) is locating into the slot at the top of the quill (I'm assuming here that your drill uses a tapered drift through a slot at the top of the quill, rather than the pair of external "U" wedges for removing the chuck and adaptor seen on some pillar drills)?
If neither of the above apply I guess it's POSSIBLE (but rather unlikely IMO) that the male taper is so badly worn that it's not seating inside the female properly, in which case a new adaptor will be needed to screw into the "top" of the chuck (not expensive, try ArecEurotrade for example - usual disclaimers).
And if none of the above apply, then I DUNNO, sorry!
HTH