I suffer from absentmindedness and constant worries during prayer, what should I do?
You should take refuge in Allah from the whispers of the devil and life worries. You should also seek Allah`s help and offer a lot of Istigfar (seeking the forgiveness of Allah). And Allah Knows Best.
Should Al-Basmalah (i.e. saying Bismillaaahi Ar-Rahmaani Ar-Raheemi) be recited after Takbeerat Al-Ihram (saying Allahuakbar) which marks the beginning of prayer?
All perfect praise be to Allah,The Lord of The Worlds A praying person is obliged to recite Al-Basmalah at the beginning of Chapter Al-Faatihah, and in every Rak`ah (unit of prayer) because it is a verse of it. And Allah Knows Best.
What is the ruling on training dogs that are of benefit?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
This is permissible because Allah The Almighty Says (What means): "They ask thee what is lawful to them (as food). Say: lawful unto you are (all) things good and pure: and what ye have taught your trained hunting animals (to catch) in the manner directed to you by Allah. eat what they catch for you, but pronounce the name of Allah over it: and fear Allah. for Allah is swift in taking account." [Al-Ma`idah/4]. However, it is prohibited to keep dogs for no benefit because Salim reported on the authority of his father that Allah's Apostle (PBUH) said: "He who kept a dog other than one meant for hunting or for watching the herd, lost two qirat of his reward every day." [Moslim]. And Allah The Almighty Knows Best.
I suffer from excessive gas, especially when I pray, and I redo my ablution more than seven times. I have obsessive thoughts about this matter, even though I went to a doctor and was given medication that did not help. What should I do?
If the release of gas stops at certain times between prayers, you should wait for that time, perform ablution, and pray. However, if it is continuous, you should perform ablution after the prayer time begins and pray, and the release of gas during the prayer is excused. And Allah The Almighty Knows Best.