Each Maneuver Must Be Evaluated Individually...

There's no way to generalize the applicability of every maneuver to every ability that grants additional attacks. Some can be used and some can't.

In your example, while the 1st-level Desert Wind martial maneuver burning blade (boost) (ToB 52) does last, like its duration says, until "End of turn," but the 2nd-level Stone Dragon martial maneuver mountain hammer (strike) (ToB 84) says, "As part of this maneuver, you make a single melee attack." That really means only one single attack gets the benefits of the martial maneuver mountain hammer, even if the target's dropped by a creature using the martial maneuver mountain hammer who has the feat Cleave (PH 92). That's because buried in the Blade Magic chapter in the section (Type) under the heading Strike there's this text:

Because strikes allow for a specific form of attack, you cannot benefit from spells or effects that grant you extra attacks when making a strike (such as the haste spell or a speed weapon). (43)

Thus an adept possessing the feat Cleave who initiates the martial maneuver mountain hammer who drops a foe does get to make the attack granted via the feat Cleave, but he gains no benefit from the martial maneuver mountain hammer when he does. To be clear, when he's granted that extra attack from the feat Cleave, the adept isn't benefiting from "extra attacks when making a strike" but benefiting from extra attacks after resolving the strike--that is, as a result of the strike.

...But Many Boosts Last Until the Turn Ends

In the heading labeled (Type) the section Boost reads, in part,

A boost is a maneuver that grants a bonus, often on attack rolls or damage rolls, for the duration of your turn. A boost always requires a swift action, usually allowing you to initiate it before unleashing a standard action or a full attack. Some boosts impart additional effects, such as stun or fatigue, to your attacks, and others provide some additional effect on an enemy you have just successfully struck in battle. If a boost affects your attacks, it applies to all of your attacks for the round in which it was initiated, but its effect ends at the end of your turn. A boost’s effect applies for its duration, no matter which weapon you might wield in that round. Even if you switch weapons in the middle of your turn, the effect of the boost applies to your new weapon as readily as the previous weapon. Each maneuver’s description gives you the details of each boost’s effect. (ToB 42)

Emphasis mine. Therefore the martial maneuver burning blade lasts until the end of the initiator's turn because it affects attacks, but the duration of 6th-level Diamond Mind martial maneuver moment of alacrity (boost) (ToB 64) remains instantaneous.

No.

Standard actions can explicitly be used as a move action

In a normal round, you can perform a standard action and a move action, or you can perform a full-round action. You can also perform one or more free actions. You can always take a move action in place of a standard action.

^{(Actions in Combat, emphasis mine)}

No action, however, has a written rule saying it can be used for a swift action. Swift actions themselves can be (must be) used for immediate action, but that’s the extent of it. For reference, the entirety of the definition of swift and immediate actions:

Swift Actions

A swift action consumes a very small amount of time, but represents a larger expenditure of effort and energy than a free action. You can perform one swift action per turn without affecting your ability to perform other actions. In that regard, a swift action is like a free action. However, you can perform only a single swift action per turn, regardless of what other actions you take. You can take a swift action any time you would normally be allowed to take a free action. Swift actions usually involve spellcasting or the activation of magic items; many characters (especially those who don't cast spells) never have an opportunity to take a swift action.

Casting a quickened spell is a swift action. In addition, casting any spell with a casting time of 1 swift action is a swift action.

Casting a spell with a casting time of 1 swift action does not provoke attacks of opportunity.

Immediate Actions

Much like a swift action, an immediate action consumes a very small amount of time, but represents a larger expenditure of effort and energy than a free action. However, unlike a swift action, an immediate action can be performed at any time — even if it's not your turn. Casting feather fall is an immediate action, since the spell can be cast at any time.

Using an immediate action on your turn is the same as using a swift action, and counts as your swift action for that turn. You cannot use another immediate action or a swift action until after your next turn if you have used an immediate action when it is not currently your turn (effectively, using an immediate action before your turn is equivalent to using your swift action for the coming turn). You also cannot use an immediate action if you are flat-footed.

The only way to get multiple swift actions in a round is to use turn undead to power the divine impetus ability of the ruby knight vindicator prestige class from Tome of Battle.