Kingdom Builder

Yes — the mandatory action is to build 3 settlements of the terrain shown on your played terrain card and they must be built successively; if no eligible hex exists you must draw a new terrain card (removing unsuitable cards) until you can build (pages 3–4).

Always build a new settlement adjacent to one of your own if possible; only if that is impossible may you place elsewhere, subject to special rules for certain extra actions (see rule 3 and the exceptions such as tower/oracle/barn) (page 4, see also page 6 for extra-action exceptions).

No, water is not a normal terrain for mandatory builds — you can only place a settlement on a water hex by using the Harbor extra action (page 4 and page 6); note the Fishermen card also does not award gold for settlements on water (page 5).

You seize a location tile immediately when you build next to its location hex (one per location), flip it to the picture side to use its extra action (once per turn), and you keep it only while at least one of your settlements remains adjacent — if you move your last adjacent settlement away you must discard the tile (page 3).

The game ends when a player has placed their last settlement from their supply, but the current round is finished so the player to the right of the start player is the last to take a turn (page 4).

No — at endgame you earn 3 gold for each castle hex where you have built at least one settlement, but you only receive 3 gold per castle hex even if you have multiple settlements adjacent to the same castle (page 3).