I find the settlement/crafting tutorials and tips in the game extremely inadequate. Is there any way I can share crafting inventory across all settlements? It's getting tiring individually collecting all the rare materials for each and every settlement... Will the local leader perk do it? Or something else?

Yep, local leader perk, the caravan lines that the perk mentions allows you to share crafting stock between settlements.

And how do I build those lines?

If Im not mistaken you assign settlers the role of trader between settlements.