User fills out a form on mobile site (not app). Is it possible to predefine his mobile phone number in the form?
At present, no. To access his mobile phone number would require a level of access to personal information that would violate privacy laws in most countries. That aside, technically you would have to allow the site to access system level information on the device that firstly isn't possible, and secondly has the potential to be abused if it were available.
If someone wants this data pre-filled, they could set their browser to pre-fill certain data, but that is a push solution from their side and other than marking the fields correctly, there is nothing that you can do to make this happen.
Summary answer: You can't due to privacy, technical, and security constraints.