If my Yveltal with "Fright Night" Ability gets KO'd, am I then able to use Exp.Share on one of my Benched Pokemon to recover one of Yveltal's Basic Energy cards?
Sorry, but no. Fright Night would still be working so Exp.Share would not enable before Yveltal hits the Discard Pile.
If Darkrai attacks with "Abyssal Sleep", can Pokemon Ranger clear the effect of flipping 2 coins when Asleep?
Asleep, Poisoned, etc. are Special Conditions, regardless of how many coins you need to flip or how much damage the poison condition does. Therefore they are not altered by Pokemon Ranger.
Source:
TPCi Rules Team (2016-11-10), TPCi Rules Team (2016-12-08)
If I used Mewtwo's "Barrier" attack last turn and this turn I play Pokemon Ranger, does that clear the effect so I can use "Barrier" again this turn?
No, Barrier does not "place an effect" to prevent its use on the next turn (unlike attacks such as "Volcanic Heat" which says "this Pokemon" cannot attack next turn). Instead, the attack does a Game State check to see if it was used last turn. Since there is no effect to clear, Pokemon Ranger won't allow you to use Barrier two turns in a row.
Source:
TPCi Rules Team (2016-11-03), TPCi Rules Team (2016-12-01)
Let's say I have Machop active with a Focus Sash attached, and my opponent's Mewtwo-EX uses "X Ball" for 360 damage with four Double Colorless Energy and a Muscle Band attached. The Focus Sash leaves Machop with 10 HP remaining. If I then use Ninja Boy to switch Machop with Pidgeot-EX and then use its "Mirror Move" attack, does Pidgeot-EX do 360 damage in return?
Yes, it would. When using Ninja Boy the amount of damage done last turn is remembered by the new Pokemon, so Mirror Move would do 360 damage to your opponent's Active Pokemon.
If I have Volcanion EX in play and I use its "Steam Up" Ability, can I then use Ninja Boy to switch it with a different Volcanion EX and use "Steam Up" from the new Volcanion EX?
No, that won't work. Even though the new Volcanion EX is a different Pokemon than the first one, it remembers the Steam Up ability was already used this turn so you cannot use it again on that Pokemon.
If a player with Exp. Share on a benched Pokemon has discarded their Active Pokemon and its attached energy due to KO from an attack and already promoted a new Active Pokemon, have they missed the opportunity to use Exp. Share?
Promoting a new Active Pokemon takes place after the knockout, so at that point it would be too late to use Exp. Share.
Say I have an Yveltal with "Fright Night" Ability as my Active Pokemon with Bursting Balloon attached, then I play Hex Maniac. What happens at the end of my opponent's turn, when they attack and do damage to Yveltal?
Hex Maniac works until the end of your opponent's turn. At the end of your opponent's turn, you check to see if Bursting Balloon gets discarded. So Bursting Balloon places the 6 damage counters, Hex Maniac's effect wears off, and then Fright Night is reactivated preventing Bursting Balloon from being discarded.
Pokemon Ranger says "remove all effects of attacks on each player and his or her Pokemon." Does that mean it gets to remove any Poison, Paralyze, etc. effects that were caused by an attack?
No, Pokemon Ranger does not remove any Special Conditions. It removes effects like "the Defending Pokemon cannot retreat", "the opponent cannot play any Item cards from his or her hand", and things like that.