Hey Nicole! A great thing about Asana is it has the project tethering (tasks can live in multiple projects), but also that moving a task from one project to another is very simple.
This guide post should walk you through it, but also you can press tab+p when in a task to either change or add a project.
And then once added to the right project you can change which column or section it's in as normal.
For your second question, you won't be able to see subtasks on a project-specific calendar as far as I know (but you do see subtasks on team calendars...weird, I know). However you can work around this by adding the subtask to the project. It seems a little counter-intuitive to add a subtask to a project it's already in, but this will ensure that you see it in the calendar view. Just go to the subtask's view and hit TAB+P and type in the project name. It'll now appear in the project view (you'll have to add it to the particular section though).
It sounds like you want to do this for all the tasks, so I might suggest you changing how you set up your project/tasks. Have a section for each email, then a main task for each item (rather than the main task being the email + subtasks).
However if you want to just keep doing it how you're doing it, I recommend using advanced search to mass-add the subtasks to your project. Advanced Search -> tasks in XYZ project -> subtasks only. Then select all of them (select first one in the list then shift-left click the last one) and type TAB+P -> add to project.