Praise be to Allah, the Lord of the World; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
1. Shaving the mustache completely is permissible according to the most correct opinion of the Muslim scholars, even though Imam Malik disliked doing so.
The appropriate way is to cut only the mustache, which hangs on the lip and leave the remaining. Removing it completely is not advisable.
As for your second and third questions, please read the Fatwa: 83145 and 81555. 4. As for the meaning of the verse; "Guard strictly (five obligatory) As-Salawat (the prayers) especially the middle Salat (i.e. the best prayer -'Asr) …"[2:238] it is a Command of Allah for Muslims to perform the prayers in their fixed times completing all precautions and obligations. The "middle prayer", the prayer of 'Asr, according to the most preponderant opinion of the scholars, is mentioned in particular due to its great importance. It does not mean that the other prayers could be neglected since the verse begins with ordering to keep all the prayers.
5. One who extends his garment beyond his anklebones commits a sin whether it is done due to pride or not. But, doing so as an act of pride is a major sin.
In the Prophetic Hadith: "One who draws one's garment arrogantly, Allah will not look towards him on the Day of Judgment". [Reported by Imams Bukhari and Muslim] This Hadith, in fact, does not restrict or limit the ruling expressed in the following Hadith: "The part of loin cloth, which is below the anklebones, is destined for the Hell-Fire". [Al-Bukhari] Another Hadith supporting this view is: "The loin cloth of a Muslim should be up to half the length of the calf of the leg. Or at the most between the calf and the ankle joint, but there is, however, no harm if it is above the ankle, (or said there is no harm). That which hangs below the ankles is destined for Hell. Allah will not look towards a person who lets down his loin cloth out of pride" [Abu Dawood].
As for the ruling, "a ruling is governed by its cause", we state that the "cause" is letting one's garment loose or down and not feeling of pride.
In addition one's ankles should not be covered by his garment. In the Hadith: "One's loin cloth should not cover one's ankles" [Ibn Majah].
As for your sixth question please read the Fatwa: 83495. 7. Praying in a place that contains pictures is permissible for the general rule of the Prophet who said: "When the time for prayers comes, a Muslim may pray wherever he may be". [Reported by Imams Bukhari and Muslim]
It is better however for a praying person to seek a place free from impurities, pictures, and anything else that could disturb him and divert his attention from prayer.
Allah knows best.