1. Power Struggles: are all cards discarded at the conclusion of the power struggle, or does each player retain the cards they had not yet played towards the next struggle? The reason I ask is because the rulebook makes reference in the examples to the Communist player withholding a leader card and intentionally tanking the power struggle; does he keep that leader until the next scoring round/power struggle?
Any remaining cards are discarded. I think the example in the rulebook the player decides he is waaaay behind in cards so he knows he is going to lose and would rather lose to a weaker attack card.
2. The Wall (Card 9): This card has a corresponding small chit for "The Wall" which gets placed on the board. Does that event chit get removed (and the event card as well) after one support check?
Put it there while The Wall event is in effect. Remove it after the Communist does a support check.
3. Gorbachev Charms the West (Card 14): Are both SPs removed from the same location or separate? Is the Support Check made against the country where the SP is removed, or can it be made against ANY space with opposing SP?
SPs may be removed from the same space or different spaces. The Support Check maybe in the same Country or a different one.
4. We are the People (Card 48): When moving the 4 Democratic SP from the Lutheran church, it's clear enough that the democrat player doesn't have to follow the adjacency rules, but does the democrat player still need to expend 2 SP to place 1 SP marker in a Communist controlled space?
No. Just move them into any spaces. Be careful that you don't set up a +3 for the Communist (adding 2 in Leipzig are safe from Support Checks).
EDIT(more complete explanation): Remember you are not spending Ops; you are just moving SPs, and there are no restrictions in the event from moving them to spaces controlled by the Communist.
5. The Crowd Turns Against Ceausescu (Card 54): When the Democrat is calculating the ops value of 3x the number of Rally cards drawn, is that only Rally cards drawn as part of the "15 Power Struggle" cards called for by the event, or does that include Rally power struggle cards he was dealt for each controlled space?
Only Rallies from the 15 he draws as part of the event are counted. Also usable leader cards he draws as part of the 15 are NOT counted.