This started recently - When I delete an e-mail on my phone or laptop is also is delted on the other device. How do I stop this ?
It should not be deleted on both, which is a feature some would like. However if you delete it on one, before you download it on the other it will disappear. Usual solution is to set to not automatically delete at all on one device, and set the other to only delete after some period such as a week, that gives you time to make sure you download it.
On your phone, check account settings, incoming settings, and make sure NEVER delete email from server is selected. I had a similar problem with my Samsung S3 when I first set up my Outlook email account on Verizon.
Hope that helps.