I am Ashkenazi and my wife is Temania. I enjoy cholent on Shabbat, and she likes jachnoon. Can one put fully cooked jachnoon into the cholent which is hot (but off of the fire) and then replace the cholent onto the flame? Also, which types of food can be re-heated on the plata (taking them from the refrigerators and placing them on the plata)?

Your question implies that a “flame” and an electric shabbat “plata” are one and the same, while halachically this is not the case. Replacing food on a plata avoids the problem of “seeming to be cooking” because no one cooks food on a weekday on an electric plata that by nature can only be used for warming already cooked food. For this reason, Rav Ovadia Yosef (Shu”t Y’Chave Daat 2, 45; see Shmirat Shabbat K’Hilchata ch.1 for a more “machmir” opinion) permits one to place, on shabbat, cold food from the refrigerator on a shabbat plata, if the food is dry and totally cooked. Others permit putting cold dry totally-cooked food (like the jachnoon) in a separate pot and putting this pot on top of another pot- like your chulent pot- that is already on the fire (not necessarily an electric shabbat plata (see Shmirat Shabbat K’Hilchata 1,36).