Hi @ElJaviRomero!
Congratulations on your landing page, I think you have done a good job!
Fixed headers together with on-page links generate overlapping problems that are difficult to solve according to what I have read (I still have no experience with them).
This possible solution is one of the ones that I find most interesting, maybe it can serve you. 
Regarding why <footer> doesn’t take up the entire bottom, it is because you have specified max-width: 1000px; for <div class = "container"> and <footer> is inside it.