Is it permissible for the person who hasn`t made wudu` (state of minor ritual impurity) to perform the Adhan?

Is a person who is in a state of Janabah (major ritual impurity due to having a marital intercourse, ejaculation, menstruation, and post-delivery impurities) sinful if he/she goes about his/her daily life activities in that state i.e. without making Ghusl (ritual bath)?

It goes without saying that a Muslim should always be in a state of ritual purity so as to be able to perform prayers and recite Quran. It is from Sunnah (Prophetic tradition) that a Muslim hastens to make Ghusl from Janabah, but he/she is not sinful in case he/she delayed that provided that he/she doesn`t miss prayers. However, it is permissible for him/her to go about their daily activities while in a state of Janabah, but had better bathe in order not to miss any prayer.

What is the ruling on performing dry ablution (tayammum) on a wall or stone?

One of the conditions for tayammum is that it be with pure, clean dust (soil). It is not valid to perform tayammum by striking stones, a wall, sand that has no dust (i.e., that does not produce dust), pebbles alone, or clay, as these are not from the earth or its same category. And Allah the Almighty knows best.

What is the ruling on using moisturizing creams on the skin during the day in Ramadan?

Using moisturizing creams on the skin does not break the fast because they do not enter the body cavity (jauf). Any absorption that occurs through the skin pores does not count as entering through an open passage.