Yes, but it will only share to workbenches within that settlement. Until you get the Local Leader perk and start linking settlements.
But yes. And don't forget to store junk, food and mods, as they will all be used by their respective stations.
Yes, at least at that single settlement.
At first I was dropping all my junk and scrapping it manually, but then I realized why the "Store All Junk" option is there on the workshop transfer. It is because you don't need to break stuff down, all the parts will be available for crafting anything (weapons, armor, chems, power armor, settlement stuff, food, etc) in that settlement, and the junk will be automatically broken down into it's components when do you craft. (for example, you need 3 screws but only have 1 in the inventory but you have a desk fan that also contains 2 screws and some steel. that fan will be broken down, you'll use the two screws and the steel is added to your inventory).
To share among all settlements, you need to get one of the perks from the Charisma line. I forget which level it is...6 or 7 I think, and I think you need the second level of that perk. Not sure, check your attribute/skill/perk tree.
Something to remember, is that you can store all the junk automatically, but the MODs, raw foods, and extra weapons and armor need to be transferred manually.
The only thing I found so far that won't scrap is the stuff like CRAM, SugerBombs, and other pre-made food. Now there is a non rad version of each but not sure where you get them or if you can "purify" them.