I had been convicted and got a letter from New Zealand immigration to leave the country. So after 9 months I'm applying for a student visa in Canada. Can someone tell me please if Canada immigration has any right to check my criminal and immigration record from New Zealand? No stamp on my passport.
If you're intending to try to hide your conviction from the Canadian immigration authorities, that is a very ill-advised strategy. You will get caught. Maybe not straight away, but it will come back to haunt you. Best to tell them up front (when they ask), then it doesn't matter whether they have the "right" to ask New Zealand about convictions or not.
Canada and New Zealand are both part of Five Eyes, so I would presume one can easily check the criminal/immigration records of the other.
Whether or not you have a stamp in your passport doesn't matter, everything is computerised these days.