Question

Indicate the pronoun person, number, gender, case, and noun function served.

The team poured a bucket of ice water over their coach to celebrate the victory.

person:

number:

gender:

case:

Answer 1

Their - their team 
Third Person - the team
Plural - because there is more than one person, they're talking about the team, not gender specific
None - they do not 

Answer 2

The pronoun you are looking for is the word THEIR.
Person: third person. Pronouns such as he, she, it, and they are considered to be third person pronouns.
Number: plural. Given that there are more than one individual on the team, the pronoun to refer to them has to be plural as well.
Gender: none. We don't know if the team consists only of boys or girls, which is why we cannot determine the gender for sure.
Case: Accusative/Object. They poured water over whom? Their coach. So the case should be indirect object.