Is it permissible for a praying person to make supplication in each Sajdah (a prostration) of obligatory prayer?
It is permissible for a praying person, whether praying individually, or in congregation, to make supplication during Sujood (prostration) in obligatory, or voluntary prayers. However, it is disliked for the Imam to do so since he is required to spare the prayer performers any sort of hardship, unless he is leading a certain group who don`t mind him extending the prayer.
Is it permissible to perform Tayammum for a month due to a medical condition that requires avoiding water?
Tayammum is permissible so long as the above excuse lasts. And Allah Knows Best.
What is the ruling on using bank cards such as Visa and MasterCard?
All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upo all of his family and comapnions It is permissible to use such cards in accordance with the following conditions: 1- The issuing body does not stipulate collecting interest upon late payments. 2- The merchant does not increase the price of the goods due to an increase in the commission collected from him by the card issuer. 3- The purchased item(s) should not be gold, silver or currency in case the card is not covered. And Allah Knows Best.
Is permissible to buy/sell with non-Muslim?
Yes buying/selling for a Muslim with non-Muslim is permissible as regards what is lawful.