Barbershop Quartet (Alexandria Harmonizers) encourages innovation:

https://youtu.be/EmCh9J-Cm3I

The Paris Convention gives inventors 6 months to file a design application in a foreign country which claims priority to earlier filed document.  

Since the PCT doesn't cover design rights, you can’t rely on a PCT application to claim priority to foreign design rights (sometimes called “industrial design rights”). 

You can, however, claim priority to a PCT application if you enter US national stage.

Any drawings that were not present in the parent utility application will be considered "new matter," and any claims that rely upon new matter will get the priority date that such new matter was added.

This means that your design application will not enjoy the benefit of the non-provisional application's earlier filing date.  Instead, the priority date of your design application will be the date that the design application was filed.  You r design application could run into trouble if there were prior art references that were published after the date that your non-provisional application was filed, but before the date that your design application was filed.  Such references could have been completely avoided if you could have claimed your design application was a "continuation of" the  earlier filed non-provisional application, as opposed to a "continuation in part" of such an application.

Yes, but you can only call the design application a "continuation" if all drawing views for the design application are present in the parent utility application.  If they are not, you will have to instead designate your design application as a "continuation in part."  The subsequently added drawings will then likely be treated as "new matter." 

For most practical purposes, the answer is no - a design application cannot claim priority to a U.S. provisional utility application.

Note that there is a tiny exception to this rule which applies when a U.S. provisional application is subsequently converted into a U.S. non-provisional application.  However, the practice of converting a U.S. provisional application into a U.S. non-provisional application is largely avoided because it cuts off up to a year of time from your patent term.

Since prosecution on the merits is closed after payment of the issue fee, if you needed the Examiner to consider the reference, you would have to file a “Petition to Withdraw From Issue.”  You could successfully file that on the Monday preceding the issue date, but it had to be done no later than 2 p.m. EST to allow sufficient time to process.