In canon you can have a magical creature as a patronus (Dumbledore had a dragon I believe) but it's very rare. I don't think animagi can be magical creatures there's certainly no canon precedent for it.

As to dinosaurs my gut instinct feels like it'd be silly but logically they are animals... When I was looking into animagus stuff for Tig it seemed that your animagus form was like your inner animal and would be a creature native to the country of your background but I would have to think that's a spiritual thing since countries are changeable and artificial. So I'd say if you have a character who was born in Australia but raised in the UK and considers the UK home they probably wouldn't get a platypus animagus form but some European animal.

I don't think a character would have to know what their animal is to become it since you don't choose the animal and if you don't know many and none fit your personality then it'd be silly.