1- You can practise any sport, but prctising judo just means trying to improve rather than describing having taken up the sport. I do judo, in fact I practise every day.
2- Only use 'the' when necessary with school. If talking generally, then don't use the definite article:
I live far from school. (my school)
I live near the school wehere they had the fire last week.
3- Do exercise- general, do exercises- a number of different ones, push-ups, etc.
I consider that most of the martial arts-- kyudo, judo, karate, tai kwon do, etc-- work best with 'practice' as they are considered more than a sport. 'Do' often appears with them, however.
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