Email is deleted of BT Server.

Yes that is how IMAP works. Your ipad or other device reflects what is in your imap webmail and directly controls it. Deleting on ipad deletes it from everywhere.

Some mail providers (outlook.com) let ypu hold only the last week or month on ipad. Some others (gmail.com) you just have to keep it there. British Telecom use Yahoo so well done even getting it to connect.

get mails back from your webmail Trash

... by the way the "Leave on Server" option normally refers to what happens when mail clients pick emails off the server using POP.

Every Mac email client I have used will delete mails from the webmail when you click Delete, unless you are only deleting them from on-the-mac offline folders. Outlook may be different.

Only the Mac has the luxury of offline folders to keep mails. Mobile devices rarely do.

If you want a general clean-up of raggedy old emails on iPad following multiple iOS upgrades, delete the email account from iPad, reboot the iPad, add the email account back. You will get a clean copy of all emails that are currently on Webmail and nothing else.

Yes. In the IMAP paradigm, the mail client works just like a window into your mail storage in the centralized server. Any change done occurs directly there and is reflected or seen on any other client peeking into it.