The problem of wrapping, to which you refer, is the rabbinic prohibition of hatmana (insulation). We cannot get into all of the details,[1] but we will touch on some of the major points, especially those that are relevant to your cases.
The gemara[2] forbids two basic types of hatmana. One type is wrapping food on Shabbat in order to maintain its heat. This rabbinic prohibition arose out of the fear that one who is so concerned about keeping the food hot might actually come to heat the food before he wraps it. The second type of hatmana is wrapping food, even before Shabbat, in a manner where heat is being added to the insulated food (mosif hevel). The reason to prohibit this type of hatmana even before Shabbat is that there is a concern that the heat-adding insulation might be done with remetz, a mixture of sand and coal, in which case one might come to stoke the coals at some later point. However, in the case of your first question, you have “the best of both worlds.” You do the hatmana before Shabbat in a simple insulation of aluminum foil, which does not add heat. Thus, it is permitted.
The answer to your subsequent question, whether you may put the wrapped challa in a warm oven, is much more complicated. The gemara, in reference to the type of hatmana that is mosif hevel, discusses insulating materials which are thermodynamic.[3] Aluminum foil does not add heat itself, but it does serve as a conduit for heat, in this case, the heat of the oven. There is a machloket among the Rishonim whether such a situation is considered mosif hevel and is forbidden even before Shabbat. The Shulchan Aruch[4] is stringent on the matter. The Magen Avraham[5] discusses the practice of putting an insulated pot on top of a hot oven and cites some of the Rishonim’s justifications for it. The Mishna Berura[6] feels that the leniency is legitimate (but not unanimous[7]) but only in a case where the heat source is no longer present and the heat is residual. Furthermore, if there is little heat left in the oven and it will dissipate before the time that you plan to take the challa out, there is even more room for leniency.[8] However, if you leave your oven on, even on a very low setting, then you should not put the wrapped challa in it for the purpose of insulation.
Rav Ovadya Yosef[9] is generally more accepting of leniency even when the heat source remains and says that that it is fine to put the insulated food on a non-adjustable heat source, such as a Shabbat hotplate. Another option that will work according to most opinions is to leave a noticeable section of the challa uncovered, so that it is not considered hatmana at all.[10]