Here I was thinking that a cactus was a cactus and it would be easy to tell what kind they are, how nieve of me

You have all given me a great starting point and I have been looking at pictures non stop ever since.

Can you mix a Gymnocalycium with a Parodia? The reason I ask is because #2's flower (from memory) does not have hair/spines on its bud, and from what I have read this would make it a Gymnocalycim. However the picture I found that most resembles my cactus is Parodia Linkii "buenekeri"

And would #1 be a Parodia Werdermanniana? That is the closest photo I could find to it.

Still would love to know what #3 is as I LOVE it so much and would like to know how to get more. It has never flowered and never had any pups so I am beginning to wonder how they "Make babies" so to speak

How old or big do the Parodia magnifica's need to be to flower or send out pups? It is about 8-9cms wide at the moment and it has not done either.

Once again thanks for all your help