You do not need to be able to see the Mage Hand to be able to use it, otherwise ATs wouldn't be able to make the hand go invisible. However, working around corners (or otherwise out of sight) would effectively impart the blinded condition to any action you were going for. As such, you wouldn't be able to interact with a target except by guessing which location it was in (unless you knew the target's location, and it was static (i.e. an unmoving object (keys hanging on an post) or a guard that's asleep in a chair)).
Nothing about the spell itself implies any sensory input gained from the hand, so unless you can see what's going on to direct it, it's going to be pretty difficult to use. As a caveat to that, however: ATs can make the hand go invisible... therefore, they have to be able to at least "feel" where it's at.
If the door was simply a one-way door that didn't actually require a key, I'd say (unless you rule that the handle requires more than 10 lbs of pressure to activate) that it would work if she could get the hand into the room.
If she was suggesting picking the lock, I would say that's not possible because she couldn't get her mage hand or lockpicks to the other side of the door... unless she casts/pushes them through the keyhole/under the door (your ruling on whether the keyhole goes all the way through (in which case, she could pick it from her end)).
RAW: With an invisible mage hand, you can do the following (AT, Mage Hand Legerdemain, PHB p. 98)
- You can stow one object the hand is holding in a container worn or
carried by another creature.
- You can retrieve an object in a container worn or carried by
another creature.
- You can use thieves' tools to pick locks and disarm traps at range.
In the spell text, it doesn't put any restriction on "any object not worn or carried," so it could definitely be used to take a crossbow bolt, or even pull the trigger prematurely.
RAI: You couldn't possibly see what you're doing with a fine lock or trap at range, so being blinded isn't an issue, because you can "feel" it through the hand. And you don't need to be able to see the hand. If she could get the tools, she could open the door from the other side.
As far as harassing people... that's pretty broad. You could apply 10 pounds of effort in quite a few fashions. Steal a handful of their arrows (and hold them up in the air (no more than 30 feet away from you)), undo their belt, tie their shoes together (or any other myriad wardrobe malfunctions), pull their hair or flick their ears(no damage), put a thumbs-up in their chair as they're about to sit down, use scissors to snip a cross/bow string (cruel, if it's a magic item - maybe only against mundane strings)... the list goes on.
To determine whether these things are valid targets of the spell, they must be included in this portion of the spell description:
The object can be a door, a box, a chest, a set of manacles, a padlock, or another object that contains a mundane or magical means that prevents access.
A target that is held shut by a mundane lock or that is stuck or barred becomes unlocked, unstuck, or unbarred.
Notably, "another object that contains a mundane or magical means that prevents access" will be how we determine special cases.
So,
- knotted rope tying up a PC
Yes. I would argue that a knot that is tying someone's hands together is functionally similar to a set of manacles and the knot could be considered a mundane means of preventing access. So long as there is a single knot because:
If the object has multiple locks only one of them is unlocked.
Locks in this case could extend to knots but you could leave that up to DM discretion.
- continuous chain without a lock that is holding a chest shut
Yes. This chain is a means of preventing access to the chest. Whether the chain magically falls to the ground or is unlinked without actually breaking the link could be up to DM discretion, but I tend to agree with the other comments suggesting that the spell doesn't actually break an object.
- buckle holding a belt together
Yes. My first thought on this one was no, but technically the belt prevents access into the trousers. I would argue that the prong on a traditional buckle is close enough to a bar on a door to be a valid target for the spell. To what extent the belt is undone is up to DM discretion.
- vine/tentacle wrapped around something (either an entry or a PC limb) (considering that manacles are a valid knock target)
Let's break this one up...
For an entry, Yes. If the vines are sufficiently obstructing a doorway to prevent access they could be considered in the same way a barred door prevents access.
For the PC's limbs, No. The reason this is different from manacles or the knotted rope is that there is no mechanism that is actually locked, barred, stuck, or in the rope's case knotted. The reason I said the chain would be valid and this would not is because for the chain to form a loop the last link made would have to be closed essentially sealing the loop. The vine or tentacle doesn't lock or tie itself, and it doesn't produce an enclosed loop.
- Fingers grasping an object
No. The target must be an object, not a creature
- heavy hatch covering an escape hole
No. I think there's an important distinction to be made here about the result of casting this spell. Nowhere in the description does it indicate that the target that is being unlocked, unstuck, or unbarred opens. A chest with a locking mechanism will become unlocked and many DMs in this case might describe the chest swinging open as a result, but RAW there is no indication that this is an inherent feature of the spell. The spell description states :
A target that is held shut by a mundane lock or that is stuck or barred becomes unlocked, unstuck, or unbarred.
And
If you choose a target that is held shut with arcane lock, that spell is suppressed for 10 minutes, during which time the target can be opened and shut normally.
Of course for a mechanical lock such as a padlock, it is usually opened due to being unlocked, but the door or chest it is preventing access to wouldn't necessarily swing open as a result.
The spell won't make the hatch swing open, and it also wouldn't make the hatch any lighter.
- glue/resin sealing a window
Yes. It's a mundane means of preventing access. Knock would definitely unstick the window.
As for the socks, you're out of luck. Unless you tie someone's hands together with them, but in that case remember that Knock would only undo one knot.
Sorry for the wall. I'm open to discuss these if you disagree.
Best Answer
"A mundane or magical means of preventing access"
The rationale your DM used was that the puzzle box is not 'locked'. However, nowhere in the description of Knock does it specifically say that it works on locks.
This is because, as per the quoted section, it undoes any means (mundane or magical) of preventing access, and the fact that it later mentions only 'unlocked, unstuck, or unbarred' is clearly not intended to be limiting, since it later only references unlocking. If it were providing limitations, you would have to rule that a door with both a bar and a lock would be immune to Knock, since the last sentence only addresses locks, which would be rather silly.
It also seems that it would only require one casting to unlock the entire puzzle box, large interconnected system or not. After all, you don't need to cast the spell for each tumbler in a lock, and even extraordinarily complicated locks (some of them get truly devilish) can be undone easily with this spell. Since complexity and number of moving parts isn't an issue, Knock would therefore have to undo the entire puzzle box at once.
Now, if you had a puzzle box with 6 sides, and each one had a separate mechanism, or if there were multiple boxes inside each other, it would require multiple castings, but it does not sound like this resembles your situation.