I would say probably not. The kind of things Mage Hand is described as being able to do is more similar to "object interaction" (like the free one you have on your turn), which falls short of the Use an Object action.
That said, a DM might rule that MH Legerdemain makes it possible, though it is not one of the listed additional things it can do.
RAW, I read it as no, as I believe list of things you can do is all you can do, since it says “the following additional tasks” and not something like, these are examples, but you can do other things, too. That said, as a DM I’d probably allow it. You can pick a lock, which usually requires two hands and much more fine motor control, so rubbing poison on something seems pretty straightforward compared to that.
Mage Hand allows for using the hand to "manipulate an object".
That sounds an awful lot like "use an object" which is an action from combat.
I would say probably not. The kind of things Mage Hand is described as being able to do is more similar to "object interaction" (like the free one you have on your turn), which falls short of the Use an Object action.
That said, a DM might rule that MH Legerdemain makes it possible, though it is not one of the listed additional things it can do.
RAW, I read it as no, as I believe list of things you can do is all you can do, since it says “the following additional tasks” and not something like, these are examples, but you can do other things, too. That said, as a DM I’d probably allow it. You can pick a lock, which usually requires two hands and much more fine motor control, so rubbing poison on something seems pretty straightforward compared to that.
With Mage Hand Legerdemain, when it is invisible, is the item that it is carrying also invisible?
No.