Hello KDG1234,
Thanks for posting. As I understand it, you have a question about a Trash icon on your Apple Watch.
For clarification, are you asking about the Trash icon you use to delete mail, or are you looking for something like a Trash/Deleted Messages option? On your Apple Watch, the Trash icon is used to delete mail as shown below: Manage mail on Apple Watch
"Delete, mark as unread or read, or flag a message
Open the Mail app on your Apple Watch, tap the message, then firmly press the display to:
- Delete a message: Tap Trash.
- If you’re looking at the message list, swipe left on the message, then tap .
- Mark a message unread or read: Tap Unread or Read.
- If you’re looking at the message list, swipe right on the message, then tap the Read or Unread button.
- Flag a message: Tap Flag. (You can also unflag a message that’s already been flagged.)
- If you’re looking at the message list, swipe left on the message, then tap .
- To change the flag style, open the Apple Watch app on your iPhone, tap My Watch, then go to Mail > Custom > Flag Style.
If you swipe on a message thread, the action you choose (Trash, Flag, Read, or Unread) applies to the entire thread."
To answer your second question, generally speaking, deleting an email on one IMAP-type account would delete it from all other devices that share the same account.
Take care.