Is it permissible for a man to marry up to four wives (polygamy in Islam) for pleasure although he can`t afford that?

It is desirable for the man to have one wife if there was no need for him to have more, if he can't afford marriage forthcoming expenses.

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.

Generally speaking, I`m dutiful to my mother and opt for obeying her. However, she chose a certain girl to be my future wife, but I`m not pleased with her choice although that girl comes from a good family and enjoys good character. Should I obey my mother or choose another girl that lives up to my expectations?

Praise be to Allah the Lord of the Worlds.

One must obey their parents in whatever is in compliance with the teachings of Sharia and within one`s capacity. However, you aren`t to blame for not marrying that girl, but it is better that you tell your mother about that and it is preferable that you perform Istikharah prayer. And Allah The Almighty Knows Best.

Is it permissible to offer the Eid sacrifice in a non-Muslim country?

Eid sacrifice is permissible anywhere, and Islamic Sharia hasn`t determined that it should be in an Islamic country, but poor Muslims should be given a share in order for it to be valid since it is an act of worship. A portion of that Eid sacrifice should be given at least to one poor Muslim, and if that wasn`t possible then the one offering it should consume it along with his family.