Would it be correct to say "to disсuss among his team"? Can we use "among" with collective noun (team, group, committee, etc) if they are in singular form? Or "among" always must be followed by plural noun and it's better to say "to discuss among his team members"?
Yes, you are right: among is mostly followed by plural nouns. So, you can say to discuss among his teams or to discuss among his team members, but it would have different meanings, I think you prefer the second meaning in your case.
In the majority cases we deal with the formal or grammatical plural. However, the team already contains the plural meaning itself (notional plural) as the word party here:
The millionaire is also believed to be among the royal party on board the yacht,... (the BNC)
So, both your cases are acceptable.
This example from the internet shows both usages:
A key ingredient to successful team-based decision-making is the sharing of information among members....
Information shared among members of a team can be classified on two dimensions: uniqueness and openness....
The more unique the information and knowledge possessed by each team member, the greater amount of information shared among the team, resulting in greater team decision-making performance.
In the UK at least, 'logical' or 'notional' concord is often used, collective nouns being given plural or singular verb agreement as is deemed more appropriate:
The team was founded in 1883.
England is wet at this time of the year.
The team were arguing amongst themselves.
England are winning 2 - 1.
This practice is not unknown in the States:
"the [New England] Revolution are reestablishing their reputation for resourcefulness and spirited play."
"the Heat were in it in the first half." [both Boston Globe]
The reduced forms 'among the team' (among the members of the team'), 'among the jury' etc are likewise commonly found on the internet.