Is it obligatory to restrict the ghusl from janabah to water only, without using soap or the like? And does touching the male organ during ghusl from janabah invalidate the ghusl and necessitate its repetition if the intention was solely to perform ghusl from janabah? And does the use of soap, toothpaste, shampoo, disinfectants, creams, or oils, or touching gasoline or the like, or looking at a woman with lust, or touching women by shaking hands or otherwise, invalidate wudu?

First, the obligatory way to perform ghusl (ritual bath) after major ritual impurity (janabah) is to use pure water. It is permissible to use soap if pure, unmixed water is poured over the body with the intention of removing janabah after using the soap. As for mixing soap with water in a way that alters the water, there are two opinions among scholars. The more cautious approach is not to purify oneself with it, even though the opinion allowing it has stronger evidence.

Second, touching the penis during ghusl does not invalidate the ghusl or necessitate its repetition. Rather, it nullifies wudu (ablution) if one had performed wudu before it. It is known that minor ritual impurity is removed when major ritual impurity is removed, even if one did not intend to remove it. Thus, performing ghusl from janabah suffices for wudu.

Third, the matters you mentioned are not among the nullifiers of wudu, except for touching a woman. However, the fatwa adopted by us is that it is not a nullifier. It is important to note the prohibition of looking at and shaking hands with non-mahram women.