Generally speaking, if a wingtip fence or a winglet is there, it's fixed and can't be moved, so there is no question of it being used before or after the others, although since it's always there I supposed you could say it's used before any of the others. I say generally because I seem to recall hearing recently of an aircraft that has a movable winglet in some manner, but that may just be my imagination.
Insofar as labeling is concerned, control surfaces that are split—an inboard and an outboard section—are usually called just that, as in the inboard ailerons and the outboard ailerons.
Different makes of aircraft may have different orders of usage in some manner, but since your image pretty much matches that of a Boeing 747-100/200 (except they have no wingtip fence or winglet), let's use them for explanation.
The inboard ailerons, are always in use. The outboard ailerons come into use when the aircraft is in slow flight (relatively speaking), in other words, when slats/flaps are deployed. It's automatic, the pilots don't have to select using the outboard ailerons specifically.
The flap tracks (what you see on the image are the "canoes" covering the actual flaps tracks) move when the flaps are deployed. The flaps will usually operate fine even if a canoe leaves the airplane in flight (happened to me once), and as I remember you're allowed to defer replacing at least one of them, but with a performance penalty.
The movement of the slats is connected to the deployment of the flaps. Any flap selection results in the inboard slats being extended. On the 747, the inboard slats extend when the flap selection handle is moved to flaps 1°. When flaps 2° is selected, the outboard slats extend.
The flaps are deployed as called for by the pilots moving the flap handle to select whatever degree of flaps they want. On the 747 there are detents at flaps up, 1°, 2°, 5°, 10°, 20°, 25°, and 30°.
The spoilers/speed brakes (whatever you want to call them—the argument still rages—are deployed by the pilots using a handle, pulling it aft deploys them, and the inboard spoilers always deploy. Whether the outboard spoilers deploy depends on aircraft speed as determined by the flap setting: no flap deployment, no outboard spoiler deployment.