They´re all common idioms in UK English, their meanings are -
SWIMMING IS NOT MY CUP OF TEA. - I don’t like swimming
I WILL BE THERE IN A TICK. - I’ll be there very soon
THAT DAY, HE JUST DID A RUNNER. - He just disappeared, ran away, took off without telling anyone
I HAVE NOT DRAWN ANYTHING FOR DONKEY'S YEARS. - I haven’t drawn anything for a very long time