How exactly do civ alerts and burrows work? =P
I'll have to be honest I've
never used alerts... But burrows...
Under the burrows menu (I always think of them as "warrens", because of the "w" key used to access them), you can create a new burrow. Then define it by "painting" (and, 'unpainting') the area that it covers, which can cross Z-levels and
doesn't need to be contiguous.
Once defined, you can then assign any number of dwarves to this (and other) burrows.
Any dwarf assigned to
any burrow will generally only accept (or fulfill) jobs and tasks where the endpoints (material/item gathering, workshop, food/drink storaes/ place from which the building/mining/eating etc is to be done) is within the combined area of the burrow(s) they are assigned to. They may
travel through non-burrowed areas, so you can't use it to stop them trying to wandering across a battlefield, but they won't try and grab socks or felled trees from that battlefield area.
What I have often done is to set up a burrow which covers the foodstocks and the dining area, and then if I have set up a burrow to restrict a certain dwarf to mining out a certain set of rooms (to override their natural tendencies of digging out in the north-west parts of the map, and maybe convince them to dig out something else that I want done in a hurry) if I assign them also to the food-burrow then they're free to wander off and get sustenance (assuming there's anything to eat/drink, of course), but then return to their high-priority job. If I
don't assign them to it, then they'll keep on going until they're really quite hungry and wander off for food (or hunt vermin), anyway. (But I usually relent, and grant them the ability when I'm happy with progress.)
If I removed them from the 'priority dig' burrow but forgot to remove them from the food burrow, then they'd probably idle (at least when not eating), unless there happened to be a suitable job (in this case, digging) somehow within the food-burrow's defined area. For that reason, at other times I've made my burrows intrinsically "dig area+eat area(+sleep area, etc)" so that I can't forget. But there's all kinds of subtleties that (with practice) you can work how you want to use (and abuse) them...
How you define the burrows and assign the dwarves, is pretty much indicated by the hints given under the burro(w) control panel. Some of the controls change the way the burrow is shown (what character, in what colour, over what background) on your map. Which you can use to make it obvious that this is a "food" burrow by putting a food-like icon in green over dark green, perhaps; or a red double-tilde over black to indicate something to do with magma. But this isn't compulsory, it's may just work better for you, on top of the text name that you give the burrow.
And, again, I've never used Alerts. The way I play, I seem to manage without them. So for their use someone else would be best to explain.