Is it wrong not to wear your proficiency badge on service uniform?

Although the "marksmanship" badge/ribbon has no value concerning "promotion points" (it won't help you get a promotion, unlike certain other ribbons/awards/medals/etc), it is still a required part of the Service Dress Uniform.

What the "marksman" badge is for is to say "Hey, I can shoot straight!". Be proud of it.

Yes. Depending on the uniform you are wearing. You would have to look up your service specific uniform manual to get a clearer answer than mine since I don't know what uniform or service you are referring to.