Correct is: "Are you satisfied with your English skills." "Do you satisfied..." doesn't work in any context grammatically. You can use these constructions, also--i.e. the requirements are being satisfied rather than the person's feelings/perception. "Do you satisfy the requirements for English skills?" "Did you satisfy the requirements for English skills." I think this a dative case issues; i.e. to whom/what is being satisfied. Either in relation to a person or in relation to something external like requirements. But, I'm not a grammar expert.