Mobile web header design ~ sticky, static or fixed headers?

On my new application I have the header static, and the footer fixed with the main menu there. A little weird but way more mobile friendly. On desktop I left it like that as well since users will want it in the same spot. Just noticed google was trying this with their new tasks app ha :P

Static, unless it has mission critical stuff.

If i'm understanding correctly you are re-creating a project that is a typical "dashboard with left sidebar" (https://dribbble.com/search?q=dashboard&s=latest) so I would start talking about the header but takin exact that into consideration.
Having that header sticky, static or fixed should depend on what should that achieve, why should that be useful to the user etc.
Typical dashboard form (with left sidebar) has the header and sidebar fixed as both contain most important navigation options/info. Only main content are is scrollable.
Facebook & Linkedin both have sticky headers as those are main navigation areas (+ they stick other areas like contacts)
Sticky top header that hides when scrolling down and shows up when scrolling down is often used on news sites where you want the user to concentrate on the content and show less distracting elements. Scrolling up in that case is seen as need to "browse" so in that case the header with navigation becomes useful again.

With your project I would keep your current setup so static header + left sidebar.

Sticky headers are always nice. On mobile, the best ones hide on scroll down, and reappear on scroll up