If Blacephalon GX uses its "Mind Blown" attack to discard a Beast Energy as one of the Fire Energy discarded, does it still get the +30 damage bonus from Beast Energy?
Yes, it does. The energy cards are chosen, then Damage is calculated before the cards are sent to the Lost Zone.
Source: TPCi Rules Team (2018-11-01)
If I use Guzzlord GX's "Eat Sloppily" attack and discard a Beast Energy {*} card, would it get attached to the Guzzlord GX, or would it go straight to the Lost Zone because it was discarded?
When "discarding the top 5 cards of your deck", any revealed Energy cards get attached to Guzzlord GX immediately, before they reach the Discard Pile. Therefore, Beast Energy {*} gets attached to Guzzlord GX rather than going to the Discard Pile or Lost Zone.
Source: TPCi Rules Team (2018-05-31)