The water in the back over flow box will feed down the tubing via gravity. No need for a pump to get it out of the box . You should invest in a ball valve to shut off the water coming from the overflow this is great for maintance. They work good for turning it off while not breaking the syphon between the inner/outer boxes.
Now I have no help as for how it will enter the sump as I'm not sure what kinda sump it is.
But here is a picture of the Pump/ skimmer section of my sump.
You'll want to use as big of a pump as the over flow will alow to get the best results. Maybe JCRIM can give you an idea of the rating the overflow has . Once you have that figured out you will want to use the soft tubing that you pictured above. IF your running a reffugium you will want to get the black tubing. this will keep it from growing algee and cloging up as easy. There will be two kinds of tubing at the hardware store. you want the softer stuf. like airline tube but bigger and thicker. the other harder stuff is for sprinklers and won't work . You'll need about 6 feet or so.depending on the sump placement. Hook this to the pump and zip tye it really tight around the outlet of the pump other wise you might end up with a water fountain. AT this point you can run it to a spraybar that will be made of pvc or a sprayer that will empty out right under the water of the main tank. I have both going .
If you have any more questions feel free to email me as then I can send you some links to other sites.