Re: about your opening a new store/about you opening a new store
Both examples are acceptable. You are correct to say that the latter would be more common in writing, but I judge the first to be the most likely to be seen in both writing and conversation.
The first uses a present active participle (very common in both writing and conversation) and the second uses a gerund (which has taken an object in this case). Both examples have a noun/pronoun following the preposition 'about', so I see no error in either.