What type of electrical boxes should I use for outdoor fixtures when fiber cement trim openings are narrow & shallow?
It would help to have a single question and focus on it , what is the question about 3 wires?  I can see 2 on the top left and a loop on the right, is the question on how to wire? 

I would use a round light fixture box inset in the wall For the upper boxes 
If the box is mounted in the wall NMB wire is ok but if the box is surface mounted then it comes down to local jurisdiction rules and amendments. 

A wall pack normally needs no box, the connections are made inside the fixture, most lanterns more common with this setup will need a round box. Metal or plastic is your choice.

You mention receptacle / GFCI yes you will need an in-use or heavy duty cover and a weather rated GFCI if the GFCI is outside (many locate the GFCI inside for longer life but with weather rated it doesn’t matter as the electronics are sealed).

I forgot to mention but many jurisdictions require tamper resistant receptacles on top of GFCI.