Hi @Matt5, thanks for taking the time to share your feedback with us!
All Task templates that you create in a project template should carry over when you create a new project from the template.
If your task templates are not copied over, could you please try to open Asana in a private/incognito window and try to create a new project from the template? If the issue persists, please contact our support team and send them the URL of the project template where you created the task templates and the project created from the template where the tasks templates where not duplicated. With this information, we will be able to have a closer look at your project setup and fix any issues.
In regards to your second question, unfortunately, task templates are not supported on mobile at the moment. This is something our product team is aware and hopefully we will implement it in future updates.
I hope this helps! Let me know if you have any other questions!