Is it permissible dance to songs that contain the Prophet's (Sallallahu Alaihi wa Sallam) name and other things like: "Salla Allah A'ala $Muhammad$$. Salla Allah Alaihi Wa Sallam". Songs also that includes the Names of Allah?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions. If what you mean is the dancing of men during feast or to show bravery in fighting, then this is lawful. It is reported by al-Bukhari and Muslim that Ayisha (Radiya Allahu Anha) said: "It was the day of 'Id when Negroes used to play with leather shields and spears. Either I requested Allah's Apostle or he himself asked me whether I would like to see the display. I replied in the affirmative. Then he let me stand behind him and my cheek was touching his cheek and he was saying, "Carry on, O Bani Arfida (i.e. Negroes)!" When I got tired, he asked me if that was enough. I replied in the affirmative and he told me to leave" . But this should be limited to feasts and celebrations. So, it is unlawful for the person to become a professional dancer. This is the reason the scholars refute the testimony of the person who takes dancing as a profession because it (dancing) reduces the honor of the person. However, dancing during Dhikr as mentioned in your question or while performing an act of worship is strictly forbidden as it is a bad innovation brought into Islam by the dissolute and perverted people. The Prophet (Sallallahu Alaihi wa Sallam) said: "Whoever beings into this faith of ours anything that is not from it, it is to be rejected" . Anyway, dancing is not lawful for men except in the above stated situations. But if what is meant is woman dancing amongst themselves, this is lawful as long as it does not lead to problems between them or temptations and provided no Haram acts accompany this dancing such as music, talking so loud that alien men can hear them, and also provided they do not expose their Awrah to one another. Allah knows best.