Custom field (product) with custom text doesn't show up in the e-mails.

Hi,

That's normal.
A custom field of the type "custom text" is meant to be displayed on the form where the fields are being displayed.
So for a custom field of the table "product", custom texts will display when you edit the product.
For custom fields of the table "item", custom texts will display on the product page.
You won't be able to display text like that on the products listing in the email of an order.

The email display options there are actually not useful. And even most of the display options there are not useful. The thing is that these options appear and disappear based on the custom field table and not based on the custom field type.

What you should do instead is this:
Create a custom field of the table "product" and of the type "text" and don't force it to a product in particular but configure it to display on the emails.
Then, in the product edition page of that product, enter your text in the custom field.
That way, that custom field data will display on the email notifications for the products where you have some text in that field.

Hi,

Unfortunately no.
That would require some customization of the email via the menu System>Emails by a developer.