Different content if a landing page is view on mobile vs desktop

Of course.

I assume you're using Guided Landing Pages.

The CSS Flexbox order: style is the best fit. Traditional float: styles may accomplish the same thing, depending on your layout. Or you can rearrange using all manner of JS.

These are assignments for your designer.

I'd add that working with Bootstrap makes this a lot easier - there are built-in classes to help "flex" (display) and "order" (position) content without needing to build it up from scratch. 

On the "order" link above, there's a list of classes with device "breakpoints" (screen size) built in to make it easy to have something be, for example, order-0 (top) for mobile and up, and order-lg-4 (4th) for "lg" (large) displays and up. The most practical way I could think of to set this up on a template without having to expose/edit the base HTML each time would be to set the mobile order in the code and then use a variable to add the breakpoint (sm, md, lg, xl) and order # (1-12) for any elements you wanted to re-arrange.