Yes — when you use the Sheriff's Office, you first discard the rightmost scoundrel in the Saloon, then the Saloon refills (a new scoundrel goes in the leftmost space), and only then do you pick your Sheriff option. So the Saloon changes every turn.
Reorganizing means moving your scoundrels to different spaces on your sheet, and you can do it only when you hire a scoundrel. The designer confirmed this applies when you hire from the discard pile too, and abilities then resolve according to the new arrangement.
A scoundrel with a white arrow instead of a poker card icon is used immediately after you use the adjacent scoundrel the arrow connects it to. It cannot be activated on its own, so a chain needs a scoundrel with a normal trigger at its start.
Yes — every player starts on the 0 space of the reputation track, and the tech value printed on the space you end on is your reputation score for the game's end.
No — the track runs from -2 to 6 and tokens stop at the ends. Card glossary entries for abilities such as Con Artist and Talkative assume these limits.
No — an ability can be used only if you can pay its cost, and losing reputation counts as a cost. At the bottom of the track you cannot use it; the rulebook glossary says this for Con Artist (cannot be used at -2 reputation).
No more than the current day number: one on day 1, two on day 2, three on day 3 (extended game). If you steal beyond that, look at the safe and abandon one of your safes back to its site; you may abandon the one you just stole.
Only marks whose number matches the safe's value count. Each matching mark is worth one extra tech to whoever steals the safe; false numbers score nothing.
Yes — Post Bail and similar effects let you free henchmen belonging to any player, so you can satisfy a card's free-a-henchman requirement without having jailed henchmen yourself. It can also be part of a deal.
The top card of any poker deck, yours or an opponent's. The glossary says to put the card back on top before deciding whether you want to shuffle that deck.