Aren’t extensions as such cannot be permanent? It comes with wall mounting nails/screws and all those marketing pictures seemed a bit misleading… But can’t say it can’t be done. Just my 2 cents.
Sorry, I’m not understanding your question/comment.
From what I can tell, the cord itself isn’t screwed in, just the outlet cover with the hinged door. The door covers the extension cord when it’s plugged in to apparently make it safer around children.
(Please note: I don’t work for Woot, I just volunteer to help out here on the forums.)
The safety aspect has been covered well enough, I think. It’s permanent enough to leave in place, but not permanent in the sense that you can’t remove the door or the extension fairly easily.
And this is genuinely a useful sort of thing for “moving” an outlet without having to modify the wall. Especially useful where you don’t want to pay for a pro to redo wiring (and a wall), or for renters who may not have that option.
The one thing that I would caution is just from experience - Low profile plugs like that have NOTHING to grab when unplugging, so just be careful not to let your fingers squeeze too tightly, and end up making contact with the plug as it is pulled out. Might only be enough to wake you up. Might be more than that. 
Five outlets but really only 4 if you use this as intended with the cover since you are covering an original outlet.
Only if you buy two will you have true 5 usable outlets (x 2) or if you have another appliance with a low profile plug and thin wire. Then you can use the original outlet to full capacity by accessing both original plug receptacles through the top and bottom slots in the cover. Just my 2🪙’s.
Are these Intertek or UL listed? FCC does not cover electrical devices for safety, only for interference with other devices, specifically communications equipment.