Jolteon

Does a BREAK Evolved Pokemon such as Raichu BREAK or Marowak BREAK still have access to the type changes from Flareon's "Flare Effect" ability or Vaporeon's "Aqua Effect" ability or Jolteon's "Electric Effect" ability? Or do those Abilities no longer apply after the Stage 1 Pokemon becomes a BREAK Evolved Pokemon?

Pokemon BREAK are their own classification, so they are not considered Stage 1 Pokemon. Although BREAK Evolved Pokemon share many of the traits of the Pokemon it evolves from, it is no longer a Pokemon of the previous stage it evolved from. Since it is no longer a Stage 1 Pokemon, the Flareon's/Vaporeon's/Jolteon's abilities do not apply.

Does Golurk's "Double Type" ability which says "As long as this Pokemon is in play it is both and type" block Flareon's "Flare Effect" ability or Vaporeon's "Aqua Effect" ability or Jolteon's "Electric Effect" ability which adds or or to any stage 1 Pokemon?

No. Golurk would have all 5 types if all of those Abilities were present.

If Flareon's "Flare Effect" ability or Vaporeon's "Aqua Effect" ability or Jolteon's "Electric Effect" ability adds Fire or Water or Electric type to a Darkness Type Pokemon, does Dangerous Energy get discarded since it says, "If this card is attached to anything other than a Pokemon, discard this card"?

No, it is not discarded. Even with the addition of another type to the Darkness Pokemon it is still also a Darkness Pokemon.

If "Flare Effect" or "Aqua Effect" or "Electric Effect" has added or or to my Ariados' type, when I use its "Poisonous Nest" Ability to poison all Active Pokemon except type, is Ariados poisoned or not?

Ariados is not poisoned, because it is still type.