As for "The shop is open" or "The shop is opened",which sentence is right?
I think this is an interesting question. We often do use the past participle form of a verb as an adjective, but as Zero's comment and kiamlaluno's answer indicate, opened is "non-standard" in OP's context.
Having said that, I think there is evidence that native speakers are trying to "regularise" things...
Picking up on my first sentence, it's worth noting that there are two "adjectival" forms derived from the verb to interest. Both are common, but they have different meanings...
I am interested - something/someone is exciting my interest
I am interesting - I am [capable of] exciting someone else's interest
*I am interest - would normally be considered completely unacceptable
Open is an adjective, and you should say "The shop is open."
Is the museum open on Sundays?
I declare this festival open.