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.
Best Answer
"But how does the rogue know its limits?"
The mage hand spell and the Mage Hand Ledgerdemain description give the general idea. Past that, the player describes what he or she wants to do, and the the DM narrates the results.
"Do they mentally KNOW it's location?"
That is not specified in the rules, so up the the DM. I rule it that the rogue just knows where it is.
Another interpretation might be the rogue can "see" an outline, like an invisible item in a cartoon is sometimes depicted.
"Can they feel through it?"
There's nothing in the rules that explicitly says they can feel through it, but the rules imply there is enough sensory feedback to accomplish the tasks listed in the description. I allow the rogue enough sensory feedback to accomplish the task, but not enough sensory feedback to accomplish something very different from the tasks listed.
"If so, does it extend to all senses of touch like temperature, pressure, texture?"
Same for these.
"I know it can't pass through objects but could they send it through a window or chimney and open a door locked on the other side?"
Maybe, depending on the situation and the DM's interpretation. It would be reasonable for the DM to give a significant additional difficulty rating or to make it several separate tasks and checks.
"Pick someones pocket from the opposite side of a busy room?"
Yes. Or rather, the rogue can try. Increased DC or disadvantage might apply, especially if vision is obscured. Or maybe it is several different checks. Maybe one to even find the pocket. Maybe the rogue gets the wrong item. It shouldn't be really easy to pick a pocket that you can't even see, but maybe not impossible. The risk of the target catching on that something is going on should be significant.
"Can they disarm people since a weapon isn't in a container?"
No, that's an attack.
"Steal a ring of keys?"
As in pick it up and carry it? Yes. As in remove them from a container? Yes. Those are all within the description.
In general, it is easy to interpret MHL very broadly, and there is nothing wrong with that. The DM has to decide where the limit is, based on what sort of campaign you and your players want. The rule of fun is always a good one. But it is also worthwhile to keep balance in mind. The Arcane Trickster has lots of other features besides MHL.
Imagine this scenario. The rogue is in a jail cell. The rogue knows the guard is sleeping around the corner and saw that the keys are on the guard's belt and earlier saw where the chair was and what the belt and keys looked like. "I use my MHL to get the keys!" "You can't even see the guard, you use MHL to feel around. Roll a perception check." "16!" "It takes you quite a while to feel where the keys are, but you also hear the guard moving in his sleep. Maybe you're tickling him. You try to remove the keys. Make a sleight of hand roll with disadvantage." "Rats, 12!" "That won't do it. You can't get the keys off. You've used up 8 rounds, you've got two tries left." "Arrgh! 8!" "Not even close. Suddenly the guard isn't making any more noise." "Did he wake up?" "How would you know?" "Try again or not, the spell's about to lapse." "21!" "Seriously, that was with disadvantage?" "Oh, right. Oh baby, yes! 20!" "You feel the keys lift off the guard's belt, and they come floating around the corner. They're within two feet of the jail cell, and the spell ends, and the keys fall to the floor. It sounds really loud. The guard yells what the!" "I reach out and grab the keys and hide them!"
To me this makes it fun. The guard is sleeping, but the rogue can't see the keys. The MHL isn't an auto-win, but the rogue gets to use it. PCs are hard to keep in jail, after all.