Should tags be inside or outside the input field

1. Do inputs have to be inside form?
2. Can I use input tag without form?
3. Which new attribute of the input element in HTML5 allows the input element to link to a form even if they are outside the original form tag?

Do inputs have to be inside form?

Yes, you can have a valid input without a form.

Can I use input tag without form?

The consensus seems to be that FORM tags are no longer required when you simply want to render a form input control. If all your input field is doing is providing a UI (user interface) hook for interactions, then you can put the input fields into the HTML without including a FORM tag.

Which new attribute of the input element in HTML5 allows the input element to link to a form even if they are outside the original form tag?

In HTML5, you can use the form attribute: A form-associated element is, by default, associated with its ancestor form element, but may have a form attribute specified to override this.