Snooptodd was pretty much dead-on with his answers, so I'm just going to expand a tiny bit. I used to be a dealer and floorperson in Atlantic City, so if I say "standard rules," I mean the rules as codified in NJ State Law. Casino practice may have deviated a little since my time there; I worked there in the early 90's.
I know on 3rd-street that the low card must bring-in, but can the low card open for a full small bet?
Yes.
Right. The rule is that the low card must bring it in for
at least $1. That means they're also allowed to make a larger bet. In a spread limit $1-$5 game, they could even open with $5.
In a $3-$6 game, if Alice brings-in in for $1, Bob completes to $3, Carl raises to $6, and Derick raises to $9, can Erick raise to $12 or does Bob's competition count as a raise (meaning that Erick can only call $9 or fold)?
Erick can make it $12. Four full bets is the cap (or five, if house rules allow five bets/four raises).
Right. This why Bob's action is called "completing." The rule is that Bob is "completing the bet" that was started by Alice. Bob did not raise.
Caveat: it's more proper to say
three raises is the cap. Technically, a bet and three calls is four bets. (Calls are bets).
On 5th-street street Alice has xx-7s-Qs-Kc and Bob has xx-7c-Qc-Kh, is the tie broken by suit or by position in relation to the button? If broken by suit, is it broken by the suite of the highest card?
On third street, bring in is determined by suit. After that, ties for first action are broken by position in relation to the dealer -- there is no button in stud.
Right. After third street, suits never, ever, ever matter.
Caveat: the position rule does not apply unless the tied hands were both dealt on the same card. If one of the hands "catches up" to the other, the lead does not change. The lead only changes when someone shows cards that are higher than the previous leader.
So in your example, the tie is broken by giving the lead to the person closer to the dealer's left - the person who was dealt the first card that made the "K,Q,7" hand.
However, consider this order: Alice has xx-7s-Qs-Kc and Bob has xx-7c-Kh-Qc. Bob had the lead on 4th street with "King, Seven," so Bob maintains the lead on 5th street. Lead does not change until the leader is bested. One proper way for a professional dealer to call it is to point to Bob's hand and say, "King heart, Queen, Seven still high," and this can confuse people - the word "heart" is thrown in there to differentiate Bob's hand from Alice's, and it should not be taken to imply that the heart matters. If the dealer knows people's names, he can also say, "Bob's King, Queen, Seven still high." Alternately, they can pull this one out: "Kigh heart, Queen, Seven retains the lead." One way or another, he is supposed to specify which K, Q, 7 he means, and if he has no other way, he can call out a suit to do so, but that does not mean that the suit matters. Technically, the dealer should NOT point and say, "this K, Q, 7 is still high," because it fails to verbally identify the hand, but I don't think anyone would ever care. In fact, most places, if the dealer just taps in front of the lead and says nothing, people are satisfied.
On 4th-street street Alice has xx-J-J, Bob has xx-A-9, and Carl has xx-5-3. If Alice opens for $3, can Bob raise to $9? If Alice opens for $6 and Bob raises to $12, can Carl raise to $18? Or does a big bet on 4th-street count as two raises?
Every player will have the option to bet/raise the big bet amount, regardless of what Alice does. So every player can make a $6 bet/raise. Each incremental increase in the bet amount counts as a raise, so again, four (or five) total bets are allowed, regardless of amount. Once the big bet has been brokered, there's no going back (can't be $3, $9, $12).
Right. The presence of the open pair allows anyone to shift the game from the small bet to the big bet, not just the person with the open pair. But like Snooptodd says, there's no going back - the general poker rule always applies: "all raises must be equal to or greater than the previous bet or raise on that round." So once someone goes big, the game has shifted. The only exception is when someone is put all-in.
On 3rd-street Alice opens, Bob calls, Carl raises and all players except Bob fold. Can Bob and Carl re-raise each other to infinity? Or are they still limited to the one-bet-three-raises rule as they did not start the hand heads-up? If the answer is that the rule still applies, does that mean that on 3rd street, that so long as there are more than two players at the table, that there is always a raising-cap on 3rd street?
I've never seen a raising war in this situation, so I don't know what happens, but my guess is any time you are heads up in a pot, regardless of whether you started that way at the beginning of that betting round's action, you can raise until one player is all in.
Again, correct. As soon as the action is heads-up, betting is uncapped, even it had already been capped! For example, the following action has proper calls by the dealer:
Alice opens, Bob raises. Carl calls.
Alice raises. Bob raises. Dealer declares "raises are now capped."
Carl folds. Dealer should declare, "heads up, there are no caps."
Alice may now raise if she wants.
Bear in mind that the purpose of capping raises is to limit pot-slamming - that its, to prevent two players from using a raising war to force a third player into endlessly calling. It's too easy for two players to collude to do this - any time one raises, the other will also raise, even with crap, just to force other players to make extra bets. As soon as the pot is heads up, this form of collusion is no longer possible, and the cap should be immediately lifted (unless the house rule is that bets are always capped even when heads-up.)
Incidentally, raising from second best is sometimes sound poker strategy in limit poker, and is not necessarily collusion. Be very careful before raising this accusation.