Have I been hacked or botted through iPad storage and Mail

Assuming that you’ve not jailbroken your iPad, it is very unlikely that the iPad has been hacked. As illustrated, your iPad is a model with the very minimum 16GB storage configuration - which will always present an issue with available internal storage. A space-constrained iPad will always be a source of frustration.

As a first step, you might force-restart your iPad - as doing so will purge/release some storage to the OS:

• On an iPad with a Home button: Press and hold the top button and the Home button at the same time. When the Apple logo appears, release both buttons.
• On other iPad models: Press and quickly release the volume up button, press and quickly release the volume down button, then press and hold the top button. When the Apple logo appears, release the button.

If your internal storage is full, your only option is to better manage the storage that you have - and delete unused Apps or unneeded data. 

These support pages should prove to be helpful:

About storage on your device and in iCloud – Apple Support

What's the difference between device storage and iCloud storage? – Apple Support

Manage your iCloud storage – Apple Support

How to check the storage on your iPhone, iPad and iPod touch – Apple Support

Clear Other storage on your iPhone or iPad - Apple Support

“Offloading” Apps can be a helpful method of creating temporary space for the software update.

https://9to5mac.com/2020/01/21/how-to-offload-apps-in-ios-to-save-space-without-deleting-their-data/

Additional information about creating sufficient space for installation of a software update can be found here:

If you need more space for an update on your iPhone, iPad, or iPod touch - Apple Support

See this:

Checklist: If you want to see if anyone else has access to your device or accounts - Apple Support

And then this:

If you think your Apple ID has been compromised - Apple Support

Finally, setup 2FA if you’ve not done so already:

Two-factor authentication for Apple ID - Apple Support

If you have followed guidance already provided, without improvement, you should perform a Factory Restore - and then restore your backup:

https://support.apple.com/HT201252

The Factory Restore process will completely reset the iPad - and install a fresh copy of the most recent version of iOS supported by your iPad.