계십니다 is formal speech level. Also, 계십니다 is only used when making a statement, while 계세요 could be a statement, question, or an order.

계십니다 is a statement not a question. As it's in written form the question should be 계십니까? 계세요 is the spoken form. So it can use as a statement as well as a question.

It's a question. The ending should be -까.