Yes, I think our prawns are the equivalent of your shrimp. We also get tiger prawns...

... and king prawns....

(I'm sure there are others too but I can't think of them!)
Oats are flattened...

Whereas oatmeal over here is ground...

"Pudding" is used as an alternative word for dessert over here.... as in "MUM! What's for pudding???" but we do have some desserts that have the term as part of the name. For example rice pudding or bread and butter pudding. So it can be specific to a name or a generic term. We also sometimes call dessert/pudding "afters", just to throw another one at you!!

Squash is the generic term over here for things like marrows and pumpkins but the only time you really hear it is when we use the term "butternut squash". The other type of marrow you mention, we always refer to as "bone marrow".
Hope that helps....