Hi ExcavatingMars,
Welcome to the Apple Support Communities!
We are happy to help with the issue you are having with your Safari tabs being closed, history being cleared, and being taken out of private mode each time you open Safari. Are there any other devices using the same Apple ID as this iPhone?
"iCloud keeps the tabs you have open in Safari up to date on your iPhone, iPad, iPod touch, and Mac. That means you can go from one device to the next and pick up browsing wherever you left off." So in your case, if there are changes being made on another device in Safari, you would see them reflect on your device. Get details in Set up and use iCloud Tabs.
You should make sure you are running the latest version of software. Learn how to Update your iPhone, iPad, or iPod touch here.
You can also check your Settings > Safari > Close Tabs. You might want to change this setting. You might have it set to "After One Day".
Cheers!