Bunny lays down (like a pancake) when I pat him

Bunny lays down (like a pancake) when I pat him

I am not sure what you mean by 'pat', if you mean the verb 'touch quickly and gently with the flat of the hand' then you are doing it wrong.

Bunnies like to be stroked. Soft pets that glide easily over the fur. I go into some detail in this answer.

As for playing with toys:

Cats and dogs like to chase things (think catch and eat prey).

Rabbits don't chase things, they will occasionally toss things. But they play different than cats and dogs. They like things to chew on and dig in.

• digging box