Emails not deleting on Iphone/Ipad

I would first check your email on your Mac and how you have your email configured.

Setting in Mail >>Accounts >>Click on the Account then look at Mailbox Behaviours (See screenshot example below) Click on each and set up your email on how you want to keep and delete emails. If emails are not being deleted from the Mac then they won't be deleted from the IMAP server and subsequently won't be deleted from the iPhone or iPad.

Have you thought about using "When Quitting Mail". If you are waiting a day then the emails on your mobile devices will not be deleted until you delete them off your Mac

You could try the other method of logging into you Webmail providers site and deleting them there for the time being until you can figure out what is going on.

You lost me on the "Store deleted messages on the server".

What option are you referring to and your ISP. If it's an option on their email servers then you are about the only one that can enable it.