You answered all the questions I had when I saw this. It does really depend on the context. Another positive thing might be that the amount of ice they are able to transfer to be used as ice cubes in a drink is less fresh water melt that would have gone into the oceans (affecting things like the AMOC), which is one of many concerns about Greenland's melting ice.
Yes, with different effects. I'm not saying this will really have a measurable influence, but melt into Greenland waters is far worse than in most other places. Just look into papers discussing the AMOC slowdown and its causes.
Relocating it into more distant water cycles kinda dilutes the dilution, so to speak. Rather than dumping a bunch of fresh water directly into salt water, it lets it trickle back slowly and gives ocean water a bit of a buffer to disolve more saline, and gives it a chance to get stuck on terra firma somehow.
I didnt expect a good explanation for this, but harvesting broken glacier isnt a bad idea on paper.