Is the mentioned method for ghusl from janabah correct, and is it permissible to use soap in it? Is it the complete ghusl or not, and what is the method for the partial ghusl, and is prayer valid with it?

The ablution (ghusl) performed in the manner described is valid and removes ritual impurity (hadath). Using soap during it does not invalidate it, nor is wudu (minor ablution) required afterwards. For a sufficient ghusl, it is enough to cover the entire body with water along with the intention. As for the complete and recommended ghusl, it is that which is performed in the manner of the Prophet, peace and blessings be upon him.