Is it possible to see a list of the settlers in a given settlement and the jobs they are assigned to? It would make it easier to pick a settler for a new job.
The Vault-Tec Workshop added a buildable item called the Vault-Tec Population Management System. This let's you management settler assignment to jobs as well as unemployed settlers. It also helps you keep track of companions.
To build it, you will find it in Workshop Mode -> Power -> Miscellaneous
If you do not have the Vault-Tec Workshop DLC but PC mods are an option for you then you can try the Don't Call Me Settler Mod which provides settler management and a few more things like auto-assigning settlers to available jobs, clearing corpses from your settlements, and tracking damaged items in your settlement.
No, unfortunately there is no overview of what all of your settlers are doing. However you can see what each individual is assigned to if you have visibility of that individual and their assigned task - this picture will show you what I mean:
This settler is only assigned to half of these carrots, another settler is doing the others, so when I target this settler is highlights half of the carrots.
There is, however, an overview of all of your settlements available in your Pip Boy, under the Data > Workshops tab:
This will warn you of any issues at each of your settlements.
Unfortunately no, there is no current settler interface within fallout 4. Like mentioned by kalina, you can see the tasks in build mode by hovering to the settler in question. To make it easier to find their tasks (especially in big places like the castle), use the tfc 1 console command (assuming you're on pc) to hover around the settlement to check if the settler indeed has an assigned work.
To make things a lot easier, you can give them certain "uniform" to know what they're working. My guards have the sack hoods, my scavengers have the gas assault mask, my provisioners have minutemen outfits, etc.