When i played the game and required those items i would put my building on hold and acquire them while I travelled.
If you put collected junk items in connected workshops their component materials are available throughout the network.
I would kill, loot and subsequently barter the loot for shipments and also barter for junk items that contained the required materials and put them in the nearest workbench for later use.
Items like guns and armour aren't shareable through the connected network.
Being on a pc I resisted the temptation of using the console to put shipments in my inventory.
When i first started playing I would tend to hoard guns and armour but after a while realised it was pointless and spent some time doing a cleanup.
I had too much to be able to sell in a short time so I sold what i could and had a big clean up day, scrapping everything I didn't want.
I put some of the rare items that i never use in storage at home plate.
From then on I stopped hoarding non junk items and disposed of them immediately.
Outfitting settlers, bartering for ammo and so on.
With regards to settlers, yes they can use things that are available to them.
If you periodically go around and check their inventory you may find some that have looted and borrowed things from storage.
They can also use power armour if they have access to power cores.
I have placed fusion cored pa suits at all settlements and sometimes the settlers will jump into them when an attack occurs.
I have found they are more likely to use them if the pa is in a pa workbench and near to where they are stationed.
Most don't stay in it forever, especially if they have duties requiring them to get out of it.
Also if you talk to them the only option is to tell them to get out of the armour.
I do have one Provisioner, though that jumped into a pa suit during an attack and continually uses it as they travel between Red Rocket and Abernathy. Provisioners never sleep.