I dont live on a farm, but I do have horses and keep them on a livery yard. My basenji often joins me at the yard to help me with the horsey duties.
Regarding basenjis and horses I have found that Maya is very curious of the horses, but also very sensible around them. When they are tied up or in the stable she will go up and talk to them (my horses are very dog friendly so always have a sniff of Maya!) but when they are walking or out in the field she keep a sensible distance from them. I have not had any issues with her getting under their feet or getting kicked. If anything she is a little wary of them when they are moving and that is only a good thing. Maya has also never touched any of the manure other than to have a sniff and wrinkle her nose in disgust
The off lead thing always seems to get a lot of opinions on here. I have walked Maya off lead from 12 weeks old when she was able to be walked. We started working on her recall in the house from day one, and then practiced in the fully enclosed dog park. A basenji will never have a 100% recall, but then neither will any other breed of dog. I personally think that my dog needs off lead exercise everyday, I couldnt give her the exercise she needs if i only walked her on a lead as she is so desperate for a really good run everytime I walk her I feel the best way for her to get that is off lead. I am lucky that I do have a "dog park" nearby that is enclosed (though with some gates that get left open by walkers/children! Very annoying) and that is ideal for giving her a quick run. But I walk her daily through the many acres of farmland behind my house and her recall has always been perfect. She is walked with my other dogs (labrador and pug) and she is always the first to come running back when I call them. I trust her recall as much as any of my dogs, she has regularly spotted rabbit/birds/deer in the field and started running after them but has always come back when I called her. I dont know if it is just my dog, the fact that I walk her with a non-basenji pack all with good recall, or because I started teaching her recall so early, but I have not had any issue with this. Obviously, there may be a day where her recall fails, so i'd never walk her off lead near a road or somewhere she could get into danger, but i think thats common sense with any breed of dog.
If your basenji usually has a reliable recall and you are sensible about not walking near roads, I think she would really benefit from a good run on all those acres!!