It means you can don the shield as a swift action, while you are using a move action to move. If you do not move, drawing a quickdraw shield is still a move action.
The phrasing follows the equivalent part about drawing a weapon:
If you have a base attack bonus of +1 or higher, you may draw a weapon as a free action combined with a regular move.
Note that this "move-and-equip"-rule also applies to readying a shield:
If you have a base attack bonus of +1 or higher, you can ready or drop a shield as a free action combined with a regular move.
This makes quickdraw shields seem incredibly useless.
However, even though it is not explicitly stated, I believe these two things are mutually exclusive, i.e. you draw either a (single) weapon, or ready a (single) shield as part of a single move action. This is backed up by the part about Two-Weapon Fighting allowing to draw two weapons at once, as a shield can also be (used as) a weapon.
The quickdraw shield then has the advantage of enabling you to move whilst drawing a weapon and strapping on your shield, at the expense of your swift action.
As to your example, a quickdraw shield does not help you in the first part, since you are not drawing a weapon as part of a move action. In any case: you can't attack in that round, since you will need to move (using your converted standard action, as you have already used your move action) in order to draw the shield as a free (or swift) action. In your notation:
- Sheathe 2H weapon (move action)
- Move, while donning the quickdraw shield (2nd move action & free action)
- Bring 1H weapon from my gloves (free action)
The other way around, the quickdraw shield DOES help. You can put away your shield as a swift action AND draw your 2H-weapon as a free action during the same move, which leaves you with a standard action to clobber your foe.
- Stow 1H with the gloves (free action)
- Move, while stowing the quickdraw shield and drawing 2H weapon (move action, swift action & free action)
No
As you can see in the photo, letting go of the handle is insufficient to free the hand, nor is it likely to cause the shield to move. Some shields have two straps and a handle making it less likely to move if you release your grip. This makes your arm instead of your hand absorb the impact on the shield.
Also by RAW, there is no mechanic for a half worn shield, it is either on or off, and requires an action to change state.
Best Answer
Yes
A shield is an item. You can pick up an item without an action (Player's Handbook p.190).
Wielding a shield, not merely holding it, increases your Armor Class by 2 (Player's Handbook p.144). Donning a shield takes an action. (PHB p.146)
PHB p.146 says that armor must be donned to benefit from it.
If we wish to be exceptionally literal, p.144 says that armor and shields are separate things. A shield is carried in one hand. It must be wielded, and the dictionary definition of wield is "To handle with skill and ease, especially a weapon or tool". Given the descriptive text on p.144 that "Anyone can put on a suit of armor or strap a shield to an arm", we can most probably assume that shields are strapped to an arm, and that this is what takes an action, and that to don a shield in its proper fashion is necessary in order to handle it "with skill and ease". I think one could make a valiant stand to rules-lawyer that donning a shield isn't necessary doesn't do anything, but the meaning seems clear.
Either way, to don is to wear. You can pick up, hold or carry a shield without going to the additional effort of wearing it. No rule forbids you from merely picking up the shield the way you would pick up any other dropped item.