Are anime characters drawn seperately?
This is actually two, or even three, questions in one.
Movements in anime start and end with keyframes, everything else are inbetweeners. 
How both keyframes and inbetweeners are drawn up is not just a matter of preference (which may impact how the final drawing comes to be), but also one of efficieny.

In your example, drawing the persons separately will allow much easier change in composition even though there is nothing against drawing the frame 'as-is' right off the bat.

For example, if the director decides that the girl needs to be a tad more to the left, of that her hand needs to be higher, it's much easier to just move the girl or reposition the hand than to draw everything from scratch (including the boy, the background, etc).

Distance as such as little to do with anything and is only used to create a sense of depth. Clouds, traffic, etc moving at different speeds to create a parallax-like effect.

Ultimately, regardless of whether or not layers are used and regardless of overlap, all characters, every single stroke even, are drawn separately.