Moon Colony Bloodbath

Buildings with an ability tied to an Action (e.g., MINE, FARM) activate whenever that Action happens; you may resolve those Building abilities before or after resolving the Action, and an Action caused by something other than Work still triggers them (see pages 4–5).

Yes — you can have duplicates of the same Building and their abilities will usually be cumulative, though a few effects (for example "ignore Paperwork") are not cumulative (page 5).

No — Perks only affect the player they belong to; adding your Perk to the Progress deck benefits only you (page 5).

You only shuffle a deck's discards to form a new deck when you need to turn/draw a card and the deck is empty; Progress cards added to the deck always go on top, and if two or more cards are added at once you shuffle those added cards (see pages 4 and 8).

When a Robot is turned over, first everyone loses the indicated number of people (losing Buildings if necessary to make up the number), and only after that do you follow the rest of the Robot's instructions (page 7).

When you lose a Building you put it into the Building discard pile, move its printed people onto your playmat, lose any boxes that were on the Building, and resolve any LOST abilities on that Building before continuing (page 7).