Does a Shield Guardian concentrate on the stored spells it casts

The Shield Guardian is easier to understand if one doesn't go looking for details that aren't there, and if one notes that it's not a mindless construct. Treat it like a normal creature, with only the alterations made explicit in its description, and a lot of creature defaults will answer these points.

1. Commanding the Shield Guardian doesn't require a bonus action, because it doesn't say it does. To command the Shield Guardian requires nothing other than simply commanding it in the everyday sense of the word: saying words to tell it what to do. (Note in particular that its languages entry is “understands commands given in any language but can't speak”.)

   It may be tempting to look at the Ranger's rules for commanding their animal companion, or similar examples where explicit actions are required: this is a trap, because the Guardian doesn't have any such wording. The actual normal case to compare this to is when monster A shouts commands to monster B, which doesn't have the limit of requiring a kind of action to do – they just do it whenever.

2. It doesn't say it can only act as commanded, and it does say that it has a focus on protecting the its master. It also has an Int of 7, so it's capable of simple reasoning at least, and probably more (7 isn't that far below average). Being unable to act unless commanded would be the unusual case that would need explicit statements, so default to normal creature handling: it does stuff on its own, following its own motivations (i.e., its single-minded focus on being a bodyguard), and also follows commands it hears from its master.

3. It acts on its own initiative count, because nothing indicates special handling regarding initiative. It has the capacity to make its own decisions (within its very narrow motives) absent commands, so it's not reliant on the amulet wearer's commands.

4. It doesn't say the stored spell is cast by the Guardian with “the same parameters”, it says “with any parameters set by the original caster”. Setting parameters is not required, then, it's at the original caster's discretion. This gives the original caster some optional extra control over the spell. The rest of the spell's parameters are up to the Shield Guardian when it casts it using normal casting procedures.

5. Commanding is done via words, not a special action that defines how the timing works. Words can be spoken during the amulet wearer's turn (or if your group has loosened the “on your turn” restriction, at any time), so the amulet wearer can issue commands any time they're able to speak. Either way, the Guardian will take action to follow its commands only when it takes its turn, as normal, since no extra wording indicates any deviation from the norm.

6. The Guardian isn't given a Bonus action or a Reaction by the Spell Storing trait, so it doesn't have one to use for this. It just does it as soon as it can, like any other order it follows or action it chooses itself. (It could use a Ready action to set up a Reaction with which to cast the spell, but that would just make it take longer to act after the situation arises, so it won't do that unless the situation is unusual in that the Guardian would get some warning and time to prepare.)

While it's not specified, the action required to cast the stored spell should be the same as the action used to cast the spell normally, and must be taken by the shield guardian.

When commanded to do so by the wearer or when a situation arises that was predefined by the spellcaster, the guardian casts the stored spell with any parameters set by the original caster, requiring no components.

So the shield guardian is not just, for example, releasing the stored spell - they are casting it.

Most spells require a single action to cast, but some spells require a bonus action, a reaction, or much more time to cast.

Not to sound obvious, but the casting time of a spell defines the time required to cast the spell. Since the guardian is casting the spell, they have to spend the appropriate amount of time.