Do I have a shrimp allergy if my dad has one?

Not inherited. You don't inherit food allergies like you would eye color or other gene based features. You can inherit a tendency to allergies, which does have a genetic component. To become allergic to any food your body must first be exposed to it and have a quirky response to it at future times, but generally not at the initial encounter.
Nope. Impossible to know until you try it or get tested. But it is not inherited.