I will likely update this post over time as a central source for the most asked Japanese purchase questions.

FAQ:
* What is that little white paper with the QR code and password that comes with my Plarail purchases?
This can be ignored, it allows those living in Japan to take a consumer feedback survey, often for the chance to win a Takara Tomy product.

* I'm going to Japan, where should I shop for Plarail?
Plarail can be found in most Toy + Hobby shops in Japan, including the Plarail store at Tokyo Station. But I also highly suggest finding your local Hobby Off store, these stock a massive amount of used Plarail trains, trucks, trackpieces, and even old sets. You can find some great gems there, just be aware that as they are preowned some engines may need repair before they will run.

* Importing from Japan
While I cannot speak for their service personally, Jauce is a popular choice among BPT members: http://www.jauce.com/

I personally use FromJapan and they have always come through, even with heavy arcade equipment.
If you wish to help me by signing up through my referral link it is: http://www.fromjapan.co.jp?afid=B21026
Otherwise: http://www.fromjapan.co.jp

Apps:
This section largely covers Android devices, however if you are on iOS you can simply copy the app name and paste it into the store in most cases.
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Google Translate: https://play.google.com/store/apps/details?id=com.google.android.apps.translate&hl=en
The Google Translate app has a feature that allows you to take a picture of Japanese text to translate. It often has trouble with fancy graphical text, but is handy for translating instructions, or reading a product name from a picture to look up online.

* Plarail Whistle Control: https://play.google.com/store/apps/details?id=com.plarail&hl=en
The official companion app for the Plarail whistle control series trains.

* Plarail Master Controller: https://play.google.com/store/apps/details?id=jp.co.takaratomy.plarailmascon&hl=en
The official companion app for the IR controller H5 Hayabusa.

* Voice Control Thomas: https://play.google.com/store/apps/details?id=jp.cp.rokumendo.thomas&hl=en
The official companion app for the voice control megaphone Thomas. Largely targeted at Japanese youngsters and passable unless you have a morbid curiosity.

Downloading Region Blocked Apps:
You can download the Android APK installer file using APKPure: https://apkpure.com
Simply copy the id section of the Google Play url and paste it in the search, for example "jp.co.takaratomy.plarailmascon". As for installing a APK there are several methods and guides around the internet, Google will be your friend in this case.
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