The usual expression is 'The shop is open'. For example, 'The shop is open between 9am and 6pm every day'. 'Open' is an adjective describing a state. It is possible to say 'The shop is opened', but it does not have the same meaning. In this sentence, 'opened' it the past participle of the verb 'open'. This is a passive construction, and it describes the action/process of opening up the shop - putting a key in the lock and opening the doors. You could say, for example, 'The shop is opened every morning by the manager, and it is closed every evening by the deputy manager'. Obviously, this is a more unusual statement to make. I presume that the statement you are looking for is the first one.

The shop is open

If the shop is "Open" when it is opened ... then it would make sense that when it is closed you would say "the shop is "Close"

You need to say, "Is the shop open?" "Has the shop opened?" if you are asking a question. If you are making a statement you can say, "The shop is open." or "The shop has opened" I have heard both used, however, as the person before said, "The shop is open" is used more. "The shop is opened" sounds a little odd, you would use, "The shops has opened" instead. This is used common as well.