If you have a read through this massive thread you will see that the problems you have mentioned have been on going since BT "updated" their email sytem.
BT Webmail Feedback v2 (post 16th April release) - BT Community
If you read this thread you will see that there have been a number of "updates" to the "update" but there are still out standing issues, including the "jumping cursor".
Webmail migration update - BT Community
A further update was due a few months ago but so far it has never materialised however a request as per this thread
Webmail Update - Release Date? - BT Community
for any update on when the update to update the update has be sought so hopefully this will happen at some point.
Meanwhile I would suggest that you install an email client/app such as the free Thunderbird email client on to your PC/Laptop and use that at least until the "update" to fix the problem is rolled out.
As you already use an email app on your tablet you will know the benefits of an email client as against a web browser to access your BTMail.
