edit: chrome doesn't warn, but browsers can re-fill the input forms when you navigate forwards again. This doesn't help if the state of the website was more complex and fails to resume.
For instance if I close this tab, where I'm typing the comment, there will be no prompt. Whereas facebook will prompt me if truly want to leave the page.
(2) The concept of a "form" is less and less clear in the realm of web apps.
In the context of html in a browser, a form isn't a concept to be debated, it's a well understood element defined in the html standard.
If an app chooses to not use html forms and instead uses something like contenteditable to create its own editing environment, then you likely have much bigger issues than the back button.
It's an application-level question, not a system question. Can only be answered with semantic knowledge of the importance of the user input.