Yes, you can take higher-level Stances at your first class level

There are several issues here.

First of all, this line is in the form of a descriptive statement, not a prescriptive one: it describes the usual case of things, rather than defining a limitation on your options. I would argue that it is there solely to help players new to the book, who are creating their first martial adept from level 1.

After all, a great many statements are made in Wizards’ products that assume you are single-classed, and starting from ECL 1 is the default assumption for the game. The Wizard’s Specialization feature says you cannot cast spells from your banned schools – but you actually can, you just need to get that ability from another class.

In addition, the line does not say “first-level martial adepts are restricted to 1st-level Stances.” It says that they “begin play” with a single 1st-level maneuver. A multiclass character taking his first level in a martial adept class after ECL 1 is not “begin[ning] play,” so the statement does not apply to him.

For that matter, taken literally, that would imply that any martial adept has only a single 1st-level Stance when the game starts – even if he started at level 20 and took Martial Stance feats repeatedly. Clearly, this is not the case, which is only further evidence that the line is not a rule, but a hint or (supposedly) helpful description.

Finally, if you rule that it does prevent higher-level Stances from being taken for your first class level, it flies in the face of the entire Tome of Battle design pattern. Tome of Battle was intentionally designed to mesh well with previous books and existing characters – that is why the Initiator Level rules were written the way they were in the first place.

Every single other method of learning any maneuvers – Stances included – allows those with higher Initiator Level to “skip” lower-level maneuvers – because Wizards finally understood how important it was to the system that characters be getting level appropriate class features, even if they multiclass. For instance, a 12th-level character, with no martial adept levels, still has an Initiator Level of 6, and can take Martial Study or Martial Stance to get a 3rd-level maneuver or stance, respectively.

This single supposed exception does not make any sense in light of the context that Tome of Battle provides, does not have the form of a prescriptive rule, and does not actually specify your first martial adept level but rather whether or not the character is “beginning play,” which really does not make much sense if taken literally.

Yes.

There are only a few requirements for using a maneuver:

• You meet its prerequisites (including Initiator Level)
• You know it
• You readied it
• You’ve been granted it, if a Crusader
• You have not expended it since the last time you recovered
• You can and do use the action required for it

As you say, this means you can use more than one per round. In fact, that is exactly how the system is intended to work: while in a Stance (you should basically always be in a Stance, unless you were ambushed while sleeping or something), you use a Boost to power yourself up, and then bash your enemy with a Strike. If you use a Counter, you give up your Boost in the following round. If you want to change Stances, that replaces your Boost and you can’t do it the same round as a Counter.