If a BMW car had a Suzuki Vitara 1.6 engine fitted is it still really an authentic BMW ?

Yes. It will just be worth a lot less though, and far harder to resell unless dirt cheap.

But in some parts of the world you make repairs with whatever is available. The Peugeot 505 I had to drive in Afghanistan in the early 1990s during the First Gulf War was powered with an old Ford Transit V4 engine. But it was still very much a Peugeot.

No. Try switching Coke with diet coke, is it still authentic?

If you shight in a turkey would it be Thanksgiving? The car would still be a BMW but it would be a lawn planter since it wouldn't run with a Vitara engine in it.

Bmw is a luxury car and weighs alot more then a suzuki. If you put a suzuki engine in a bmw you would make it very slow and underpowered.

For registration purposes, it is still a BMW. To a collector, it is not authentic.

It is like if you made repairs with Chinese knock-off parts

No, of course not. It doesn't matter if it was replacing a PSA/BMW 1.6 engine or not. If you put the ears of a German Shepard on a Poodle would it be an authentic Poodle? Same difference.