Original: Although being a poor student, Tom studied very well.
Correction: Although he was a poor student, Tom studied very well.
"Although" is followed by a clause, not a gerund phrase.
Original: Despite the fact that the bad weather, she went to school on time.
Correction: Despite the bad weather, she went to school on time.
"Despite the fact that" is redundant. "Despite" can be used directly.
Original: Although my sickness, my mother told me to go to school.
Correction: Although I was sick, my mother told me to go to school.
"Although" is followed by a clause, not a noun.
Original: Although Tom’s bad grade, he was admitted to the university.
Correction: Although Tom had a bad grade, he was admitted to the university.
"Although" is followed by a clause, not a noun phrase.
Original: Although her physical handicap, she has become a successful woman.
Correction: Despite her physical handicap, she has become a successful woman.
"Despite" is more suitable than "Although" in this context. "Although" would require a clause.