You don't need to add "the" before the name of a weapon in a page. You also don't have to add "weapon" after the slot type in a weapon page, it already knows which slot the weapon is in just by typing "Primary" or "Special".
Most articles should start with the word "the" unless it is a person. In regards to the slot type, if would have bothered to compare the Exotic Auto Rifle articles before and after my edits, Overlord Nazo, you would have realized there was problem.
In terms of article names, the question is addressed in the Manual of Style. Titles should not begin with "the" or contain any other article or coordinating conjunction unless -- and ONLY unless -- the title contains the word "The," such as The Last Word. This is not a matter of personal preference, but rather an already-addressed issue in the MoS.
In terms of the first sentence of an article, I think that is far more an issue of personal preference. Proper grammar does not necessarily require the use of the word "the" when referring to the proper name given to a weapon. You wouldn't refer to "the Excalibur sword" -- it's just "Excalibur." At the same time, some of these weapons are more along the lines of model names, like a car, and there, use of the word "the" is appropriate. I don't think there's one rule here -- use common sense. "Gjallarhorn" probably doesn't need a "the," but "the Suros Regime" certainly could.