Illegal tyres are 3pts each on the licence so that would ultimately influence me, but if they are still legal then they pass the MOT. If all you're doing is crunching miles and you can live with the handling issues, then I'd leave them on until either you want to ride the bike for fun, or you're planning something like a trip to the S of France where they may not make the distance.
Chain... you mention 8k in your care but what state is the chain in and how many miles total are on the bike? 10k is barely run in for a reasonably well looked after X ring chain - the last new one on the Hornet I adjusted about 500 miles after I fitted it and the next time I adjusted it was 10,000 miles later - I finally replaced it about 40k when it started to need adjusting every thousand miles and had developed some tight spots. With the chain oiler, one chain actually made it to the end of the adjustment and was still beautifully smooth!
Why do you think it might snap? Since 1976 I've had one chain snap in about 83 (a cheap, no-name chain supplied by a very well-known mail order company years back when I ordered a DID) and one split link fail in about 95 on a 750 (I shouldn't have used it but my brother had nicked my chain rivitting tool without my knowledge). It's true they can do a lot of damage if they snap, but it's really not a common occurance if the chain is the right one for the job, in decent condition and properly adjusted - the side plates and pins are massively strong. Racing chains snap on TV but they are lighter but then usually get thrown away after every couple of meetings, plus racers are snapping the throttle open at every start and out of every corner.
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