I've never heard of an apartment with a yard. Townhouse or condo maybe, but apartments don't have yards.
I used to live in an apartment with a yard. The property had an apartment building (12 units), a parking lot, and a yard that we were all allowed to use. Considering that small children played in that yard sometimes, it was a good thing no chickens were pooping in it.
So now you have "heard of" an apartment with a yard.
If they do have an actual yard, tell them fences make good neighbors and they should build one. You're not disrupting your lifestyle because they moved in.
That would depend on the laws in their area.
Some states have laws that the animal owner needs to build a fence to keep their own animals on their own property. (OP is in Tennessee, and it looks like that is the kind of law Tennessee has)
Some other states have laws that allow animals to roam freely, and people have to fence their own property if they want to keep those animals out. (That appears to be the case in Texas, where
@Mason Farm and Ranch is located.)
And no matter what the state law permits, it is common for counties or cities to make more stringent laws. So typically people have to follow whatever is the most restrictive set of laws or rules for their area (state, county, city, HOA, etc.)
Telling someone what they have to do, or do not have to do, can be badly wrong if you are basing it on the laws where you live and they are somewhere different!