HTML5 is supported by all current browsers? including mobiles?

Answer 1

Yes it's the standard.

Answer 2

Yes, mostly ( some cross-browsers inconsistences will still be there ^^ ), and mobiles devices have taken charge of leading the last evolutions ( responsive design waited for them: even if percentage unit was available since start, web pages have little beneficited, web designers getting used to fixed size layouts, although the arrival of DHTML ( Dynamic Html ) and 'web 2.0'...