Yes, you can move settlers to different settlements. On XBox One, go into build mode, highlight the settler, press "X". A list will appear of the options you can send them to.
You won't be able to send settlers to locations which have reached max capacity for your level (CHR + 10) and these will be grayed out on the list.
To build troughs, if memory serves, this is an item listed under food/water. Go to the section with the scrap table and select it. There are a few additional options there (including the fast travel mat). It's definitely under the Resources > Misc section.
Odd, given how much I've built, you'd think I'd have this memorized by now. 1.4 did change some things, too, so that's got me all fizzled.
Hope this helps.
PS: You can't move settlers who were originally part of the settlement. If they have names, you can't move them. The two settlers at Oberland Station also cannot be moved.
You can only move those who came to the settlement on their own.