Neko Syndicate

You must start on one of the two action boxes on your lieutenants card and after activating an action you always move your leader to one of the two boxes on the card immediately below the box you are on, repeating until there is no card below (so no jumping to non-adjacent boxes). (p.5)

An action may be activated up to a number of times equal to the level that action occupies in your pyramidal structure (lieutenants=Level 1, lowest possible level=Level 4), e.g., an action on Level 3 can be used up to 3 times during your walk. (p.5)

Yes — placing a minion with the COO adds it into your pyramid and, since the Command phase continues descending the chain of command, you may then choose to activate that card's actions (they are optional) as you pass through them. (p.7)

Sashimi is fulfilled automatically whenever a matching cube is in a top neighborhood and a sashimi slot exists, but nigiri require performing the Cook action to combine rice with a cube before they count as delivered. (p.8–9)

The Delivery lady moves non-delivered cubes vertically between adjacent neighborhoods (up or down one step) up to the action's level, while the Subway operator moves a non-delivered cube to any neighborhood that has a subway station on the same line letter as the cube's current neighborhood, also up to the action's level. (p.8–9)

For the pyramid you total the prestige modifiers on each level (deliveries, completed-card bonuses, penalties for loose cubes, missing or empty cards) then multiply each level by its multiplier (Level 1 x4, Level 2 x3, Level 3 x2, Level 4 x1); mission points come from your scoring markers on the Kumichō path plus position bonuses (5/3/1/0) for each mission. (p.10, p.12)