U can un-check the green mark to not get advertised.
Yes .. But I think maybe it costs coins.
I also notice if I put something really good in the stall . Like mallets, deeds, planks etc it must get advertised because it all gets bought up with basic stuff in the shop.
Sometimes I do it on purpose. It i have filled the shop with crops and to,clear down my barn and the shop just stays full I will put a couple of expansion items in a box and stuff clears out