Around here trey are made to resist a full grown animal and need to be pretty strong. So instead of tearing out the wall just build your new wall about 12" in front of it and save all the labor of the tear out, which could be extensive if trying to pull nails out of hardwood. If your stalls are softwood, then tear it out and locate the new wall far into the stall.
Framing a wall is best down layind down, horizontally and then just tip it up and block or wedge it in place at the top. iIf the bottom will be in dirt, then you'll need to dig a trench and either set in a 6" X 8" landscape timber or other large timber to secure the base...and then there's alway a concrete "footer" . If the ground freezes, but I doubt that, it will heave and move the wall around.
AS far as selling farm tables, they are often made wil "reclaimed" barn wood and rustic, rather than new lumber. OR you can have your new lumber rough sawn, then skip planed to just make it a little smoother, but not like finished wood. It should have some ripples and saw marks for character.
A search of Farm Tables "images" and you will get some ideas:
If you can use "rough sawn" lumber you will save a lot on the materials cost...whether they will sell depends on your craftsmanship, the "look" and the finish. An oil type finish rather than a film type finish like varnish will make it easier to maintain. Go to a few local sawyers and get some prices, be sure to tell them what you are making and that you are just starting out. They may help out with a price break and if and when you come back for more, then they have a "repeat" customer. Form a relationship/friendship and that will always serve you both well. Ask me how I know this....