I have this problem too... my ipad mini wont let me delete any messages from my hotmail account... it just says "unable to trash messages" but I am able to do it fine from my iphone. This only started over xmas. My ipad has also lost all my contact details... it says no contacts to display... but they are all still there on my phone.
I have tried backing up my phone to icloud first, then backing up the ipad but it still wont fix it.
Something you could try that I did supersleuther to fix my message delete problem is go into you mail account on iPad so that it shows all your folders for that account,and click on edit.Now I had trash folder already but I deleted it and it automatically installed a new one straight away. Since then my ipad deletes the mail just like it use to.