Whenever I am on any application, be it safari, word, or any other, mail will randomly split screen with the application, even though I am not opening mail. This happens regardless of me having mail come through. It isn't split screening because I click something. I could be typing on word and mail will open to all my emails. Is there any way I can prevent mail from doing this on its own?
Hmmm. Say in Safari if you hit an email link it should open a new Mail pane by default. It could very well be coded on the back-end of the website to initiate a split screen(?) I have had it happen to me unexpectedly. I chalked it up to a bug, but never tried to drill down on the issue.
For ex. when it happens
Quit full screen mode —this split the apps connection. Quit Safari, quit Mail and relaunch both. Put both back in full screen .
If you do this test as you go and hopefully you will not have the issue again for a long time.
You can look over the ref and trackpad preference setting—for some trackpad /multi-touch/Force-touch trigger/
Use two Mac apps side by side in Split View
https://support.apple.com/en-us/HT204948
It seems odd that multiple apps on your machine trigger Mail. unless it is a email link/share. No easy answer.
I can say one-off anomalies like yours—reinstalling the combo update has been known to resolve issues not easily account for—You can download and reinstall it right on top of your existing macOS 10.14.3
Download macOS Mojave 10.14.3 Combo Update - Apple Support
Always have a current backup.