Verified answer

First of all you need to separate the two sentences for better understanding them

んなもん知るかよ!

んなもん---> そんなもの which means: "something like that/such a thing"

知る means to know か is a sentence final particle that makes a question, and よ is a sentence final particle that adds the subject's attitude.

知るかよ is a bit rude and means: "How would I know/Like hell I would know"

勝手にやってよ！

勝手 in this case means: as you please

やる means to do (or to act in this case would work too) やって it's the present continuous doing/acting

The whole sentence translated is:

"How would I know that!/Like hell I'd know such a thing!

"You are acting as you please!"

Hope this helps c:

I have translated it to;

"Doing without permission or I'll know mon such do."

Which means means;

"Doing without permission is not something I thought you'd do."

You're on the right lines!

"もの" means "thing". "んなもん" means "mon such do". To answer your question, no. "Mon such do" is not the same as "thing".

I hope I've helped! :)

Looks like it's fukui-ben

そんなもの → ほんなもん、んなもん