How to increase the size of my logo when using the navigation as header?

Hi Heath,

When the navigation as header option is activated, the logo size is controlled by theMenu Item Height at customizer > layout > primary navigation.

Also if the logo size increases will that change get the size of the search and menu icons?

No, the search and menu goggle icons will stay at the same size.

If you want to increase their size, try this CSS:

.menu-bar-items svg, .menu-toggle svg {
    width: 2em;
    height: auto;
}