""""""""The Klein bottle shown is not a fake.""""""""""""

The Klein bottle is a concept of a bottle that contains itself..

"""""""" In your model you need to make 2 holes. One where the naked edge is and one at the base."""""""""

At some point, the "surface" would have to travel through itself.. This is not possible. Could you demonstrate with a model about the extra holes you are refering too?

Sure you can blob glass together at that conundrum, but it is not a true "klein bottle".