If a USPTO PPA is filed on April 15, 2017 then do I have until April 15, 2018 to file a non provisional application with the EPO and each country's patent office?
Correct.
This is because all of the countries you mention are members of the Paris Convention (1883). The Paris Convention provides at article 4(A)(1):
Any person who has duly filed an application for a patent … in one of the countries of the Union, or his successor in title, shall enjoy, for the purpose of filing in the other countries, a right of priority during the periods hereinafter fixed.
Further, article 4(C)(1) provides:
The periods of priority referred to above shall be twelve months for patents and utility models, and six months for industrial designs and trademarks.
A provisional patent application is an application for a patent filed in one of the countries of the Union (that is, the US). The applicant therefore is entitled to a period of priority in every other country of 12 months. This means that an application filed in a second country within 12 months which claims priority to the provisional application will be deemed (for the purposes of prior art) to have been filed in the second country on the same day as the provisional application.
The reason the 12 months doesn't restart when you file a non-provisional is because of article 4(C)(2), which provides:
These periods shall start from the date of filing of the first application; the day of filing shall not be included in the period.
A non-provisional application (which relies on an earlier-filed provisional application) is not "the first application".
And then comes the PCT
As an alternative (or additionally, if you have money to burn), you can file a PCT application within 12 months of your provisional instead of filing applications directly in the foreign countries. This PCT is deemed to be filed in every designated state (for the purposes of a Convention priority claim), which includes all of the countries you mentioned. By 30–31 months of your provisional, you can then file national phase entries in your selected states. These national phase entries will then have a valid priority claim to your provisional application.
This allows you to defer the cost associated with the various national filings for an additional 18–19 months. Though it also adds the cost of filing a PCT application.
Experience
I have indeed filed a US provisional then a bunch of foreigns claiming priority to the US provisional. I have even co-filed a US provisional and a UK application, both of which were then only used for priority to file a PCT application which then ended up entering national phase only in US and EP. That was a particularly weird and expensive arrangement.
