Yes, you are right in thinking that 'The cafe has been opened for about ten minutes' is incorrect. In the first sentence, 'open' is an adjective, referring to the state of the cafe and how long it has been in this state. In the phrase 'has been opened', the word 'opened' is the past participle of the verb 'to open'. Obviously, the action of opening only takes a few moments - it cannot describe a continuing state, so it cannot be used with the time phrase 'for about ten minutes'.

It's a good question, because "closed" is the opposite of both "open" and "opened". "Yesterday, the shopkeeper opened the shop at 9am and closed it at 6pm." [verb forms] "Yesterday, the shop was open between 9am and 6pm. If you had gone there at 7pm, it would have been closed." [adjectives]

You are correct. In this case, word "opened" refers to the action of opening the store. It isn't a continuous action. "Opened" refers to the state of being. Since the cafe is not closed, it is open.

Can whoever gave me a downvote please explain why?

Alternatively..... The cafe opened about 10 minutes ago.