The first is correct. 'reopen' is still a verb. The sentence is using the future passive - 'will be reopen'. Both options in your 2nd sentence are correct. First is using the passive voice, the 2nd is active voice.

In number 1, you only need to say "the store will reopen for business soon" (you do not need the "be"). So, in that case, "reopen" is strictly a verb :-)