Here’s the real answer for based:

“Based” (corruption of base head - from someone who smokes base - street name for crack cocaine) was popular as an insult in rap / African American circles in the early 00s

Rapper Lil B got called it and decided on a whim to pretend the meaning was changed to mean something positive, started using it in this way, it caught on - mostly through the new York scene and its attendant twitter following

As all slang does in the last ~100-150 years, passed from black people to everyone.

Brain pilled is a reference to The Matrix f/t Keanu Reeves in which Morpheus - whose namesake is the God of dreams - offers to wake up Neo from his fake reality by taking the red pill - leading to the phrase "red pilled" meaning (a right wing variant of) "woke." 

Over time [x]-pilled became slang like how Watergate/ [x]-gate became a suffix to imply an imbrolglio.