Is Zakah (obligatory charity) due on the items used in the trading process such as: cars , shops etc..?
No Zakah is due on equipments used in the trading process such as cars and the like.
Who is responsible for performing the aqiqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The one upon whom the 'aqīqah is incumbent is whoever is obligated to financially maintain the newborn — whether the father, paternal grandfather, or mother. It is to be performed from their own wealth, not from the wealth of the newborn child.
As for one upon whom the financial maintenance of the newborn is not obligatory, they may not perform the 'aqīqah except with the permission of the one upon whom it is obligatory — namely, the father. And Allah Almighty knows best.
What should someone do if they fasted for 30 days in their country, then traveled to a place where people are still fasting?
If a person completes 30 days of fasting in their country and then travels to another country where people are still fasting, they should continue fasting with them until they observe Eid. Even if they have already completed 30 days, he/she should abstain from eating and drinking and join the people of that country because he/she has now become part of that community.
What is the ruling on performing Tarawih in sets of four rak‘ahs with only one Tasleem?
It is not permissible to combine more than two rak‘ahs with a single Tasleem in Tarawih prayer. Whoever does so, their prayer is invalid. Shaykh al-Islam Imam Muhammad al-Ramli (may Allah have mercy on him) stated: "If a person prays four rak‘ahs of the Tarawih prayer with a single Tasleem, it is not valid if they did so intentionally and with knowledge [of the prohibition]. Otherwise, it becomes an 'absolute voluntary prayer' (nafl mutlaq); because it is contrary to what has been prescribed." [Nihayat al-Muhtaj, Vol.2/P.127].