Is it necessary to perform ablution (wudu') or dry ablution (tayammum) if one's feet are burned, and does a wet dream necessitate a ritual bath (ghusl) despite these burns that prevent walking?

If washing the burned limb is harmful or delays healing, then it is not obligatory to wash it. In Wudu', if the injured limb has a splint, wipe over it. If not, then rely on Tayammum for the injured limb when its turn comes, while observing the proper sequence. As for Ghusl from Janabah, if washing the injured limb is harmful, then wash the rest of the body and perform Tayammum for the injured limb. Sequence is not a condition in Ghusl.