'It's on at 5 o'clock' or 'It's on in five minutes.'
As for your second question, I'll give you an answer from a British English perspective. Apart from films, news and weather reports, most things you see on TV can be called TV programmes. For example, documentaries, dramas, discussions, soap operas and so on, are all TV programmes. In British English, 'TV show' suggests light entertainment - music, dance and celebrity interviews, for example, often with a celebrity host.
In American English, the meaning of the word 'show' is much broader, and can be used to cover many of the things that British English would not call a 'show'. A soap opera or drama series, for example, would be a 'TV programme' in GBE but a 'TV show' in AE.
I hope that helps.