Just a Bill
No, I said "oh, brother," not "go hover."
New to BGG and Cosmic Encounter.
If I play the Fido Super Flare (allowing me to fetch all the discarded encounter cards and pass them out as I choose), do I still draw cards (or retrieve ships from the warp) for each card that is accepted (Fido Alien Power)?
Yes, the intent is to extend the base power from just "one card" to "any or all cards."
Perhaps I don't understand how using a Super Flare interacts with using an Alien Power. Are they independent of each other ... or are they presumed to stack insofar as they are consistent ...?
Both. Some flares offer an independent effect, while others extend the base power in some way. After you've played a few times you'll develop a feel for which is which. One way you can sometimes identify the latter is by noting if the Super flare repeats a "flavor word" from the base power. For example, Super Fido uses the word fetch as a callback, Super Loser repeats upset, Super Chosen references drawing for divine intervention, Super Cudgel smashes multiple players, Super Arcade sadly treats us to another pwn, and so on.
As a general rule of thumb, I'd say it's safe to assume that if a Super flare could leverage the base power, it probably does.