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.
Source: TPCi Rules Team (2015-10-29)

Relevant cards

Note: All applicable cards may not be listed below.
XY7_13
XY7_22
XY7_26