Q: Password protected browser

Hello zus70,

Thank you for using Apple Support Communities. 

I see you are looking for a free browser that will allow password protected browsing. While I am not aware of a browser to recommend, I can offer you a couple of options that may accomplish what you want. 

You can clear your browsing history when you are through using the iPad. 

Clear information from your device
To clear your history and cookies from Safari in iOS 8, tap Settings > Safari > Clear History and Website Data. In iOS 7 or earlier, tap Clear History and tap Clear Cookies and Data.
To clear other stored information from Safari, tap Settings > Safari > Advanced > Website Data > Remove All Website Data.

That is from this support article:

Safari web settings on your iPhone, iPad, or iPod touch - Apple Support

Or you can enable Private Browsing and visit sites without creating history. See this article for for the steps:

Turn Private Browsing on or off on your iPhone, iPad, or iPod touch - Apple Support

Cheers