1) Water wells do create purified water for crafting (each water well outputs 3 units of water). You can also make purifiers at settlements where there are sources of natural water (streams/rivers/the ocean) if you have a rank in the Science perk (the smaller purifier might be available from the start, not sure).
2) In the Trade screen you need to select an equip-able item on the settler's side of the screen and then one of the hotkeys at the bottom of the screen will tell you which button to push to have the settler equip it (think it's T on PC). To get them to guard a place you need to set down some guard posts and, in build mode, go up to a settler, press the Command button, walk over to a guard post, and press the Assign command. 1 Settler can man 3 guard posts (the 1 you select and the 2 nearest ones, this part is automatic).
3) All crops can be grown at any settlement (excluding Boston Airport), but by default, different settlements focus on different crops until you plant new crops for them to tend.
4) You might want to pop a Rad-X and have a RadAway handy, but it's quite doable, just dive where the bubbles are.