We are permitted to put into a Kli Rishon NOT Al Haesh a cooked solid food or a cooked and still warm liquid? After doing so, May I put the Kli Rishon then again on the fire??? (Of course while keeping the 5 conditions covered fire / still warm / completely cooked / intention to return / keeping in one’s hand)

A cooked solid food or liquid still hot may not be put in a Kli Rishon not Al Haesh if one intends to put it back on the fire. If one has no such intention, some allow, and some forbid. Rabbi Chaim Katz