Is it muter to move pots on the blech closer to the flames?

In the Iggros Moshe [1] it says that if the food is fully cooked and situated on the blech on a spot that is yad soledes bo, [2] one may move the food closer to the flames. See also Sefer Sh’miras Shabbos Kehilchaso 1-footnote 111. The same applies to moving a pot on a hot plate to a hotter spot.

[A blech is an iron or copper sheet placed over the flames].

By mistake I took the cholent pot off the blech thinking that it was the soup pot, may I put the cholent pot back?

This is a difficult one, and there are various opinions on this matter. One school of thought understands that since you did not intend on returning the pot of food in your hands, it may not be returned once it has been set down. If still in one's hands it may be returned, based on the halacha that one may return food if all conditions were adhered to, save for either holding in one's hands or intention to return, see shiur #37.

The other school understands that since your intention was never to remove this particular pot, the fact that it is in one's hands is of no consequence and it is as if it never left the heat source.

HaRav Shlomo Zalman Auerbach ztz”l [3] holds that one may return the food, see the reference in the footnote.

If the flames or electricity has gone out from under my pots, may I take the pots to a neighbor’s blech or hot plate?

Yes you may. Since you never took your mind off heating the food, it is as if you are standing all the time holding the pots in your hand with the intention of returning them to the fire. [4] Here too the other chazora conditions must be kept, namely the food is fully cooked and still warm.

If the cholent is burning, what may be done to save it?

Option #1. Move the cholent away from the heat source, or place a metal plate below the pot. [5]

Option #2. According to the Sephardim: there is a machlokes amongst the poskim as to whether one may pour boiling water from the urn into another pot that is on the fire, [6]

which means that it is not simple to permit pouring from the urn into the cholent.

According to the Ashkenazim: it is mutar to pour hot water from an urn on a blech, or from an electric urn, directly into the cholent pot. HaRav Shlomo Zalman Auerbach ztz”l [7] holds that it is also muter to pour from the urn into a cup and from the cup into the cholent pot. The cholent must be on a blech or hot plate in order for one to add hot water to it. If possible one should lift the cholent from the heat source before adding the water and then set it down. [8]

If the fire extinguished under the blech, may I ask a non-Jew to relight the fire?

Dealing with issues addressing non-Jews is tricky, since many are under the pretence that everything is permitted, especially when oneg Shabbos is involved.

One may not ask a non-Jew to relight the fire because lighting a fire is an issur d'oraisso (a Torah prohibition) and the halacha is that one is forbidden to ask a non-Jew to do an issur d'oraisso even for the sake of a mitzvah, unless in dire circumstances, where a Rav should be asked. [9] If a non-Jew relit the fire on his accord and the food was still warm, it may be eaten. [10]

Hatmana

Is one permitted to put a challah, wrapped in foil, into the oven before Shabbos (and the oven is either on or off)?

The problem of totally wrapping a challah is the issue of hatmana – meaning enwrapping. In simon 257:1 we find that one is permitted to do hatmana before Shabbos in towels etc. if there is no heat source present. If a heat source is present, one may not entirely wrap an item even before Shabbos and all the more so on Shabbos. Therefore, the answer to this common question must be divided as follows:

1. If the challah is not entirely [11] enwrapped in the aluminum foil it is permitted even if the oven is turned on.

2. If the challah is entirely enwrapped in foil, it depends:

a. If one’s intention is to enhance the heat, it is forbidden even if the oven is turned off. [12]

b. It might be permitted if one’s intention is only to prevent the challah from drying out, because one's intention is not to store heat and a rav should be asked. However, the correct way is to leave the foil a little open and not entirely enwrap the challah. [13]

Does the same apply to placing it on pots or on the urn?

Yes it does. If one wishes to warm challos before a meal, they may be placed on top of an urn or on top of other pots. If the challos are wrapped in aluminum foil, one should expose a noticeable section of the challah and thus avoid the issue of hatmana. If one's purpose is merely to prevent the challos from drying out, one need not expose a section of the challos.