Vague questions yield vague answers. I dislike that sort of thing.
Do Japanese people exhibit teamwork a lot? Yes, it is practically built into life here. However, what spirit the team members exhibit may depend on the situation.
Case 1.
My wife was obligated to work with other mamas at the kindergarten to plan a vendor booth for summer festival. They put in several days together cutting out decorations and deciding what to sell, and on the day, each spent 15 minutes in the booth (after they jointly set it up). On that day, they were all smiles for the sake of the kids and crowd. At home, my wife quietly complained about the time needed to do the work, and that our family was obligated to buy tickets for the food at that vendor (in addition to being free to buy other tickets).
Case 2
My university staff meetings are held monthly. People feel an obligation to attend, even though all that really gets done is listen to the leader read minutes of several meetings nobody else attended, just so we are all updates. Questions and answers may follow, but not many are forthcoming. Attendance is not mandatory, but it is still taken, and it may reflect on one's performance reviews for promotion. Nobody really seems to have any "team spirit".
Case 3
The university has an annual cleaning day outside. It's only a couple of hours, but email is sent around telling everyone to join in. People begrudgingly do it, but not all.
Case 4
Private high school. Annual festival requires days of planning after classes with the teachers' assistance. Tens of thousands of dollars are spent for a day and a half. Skits are performed for awards. Two days of regular school time are lost for setup and cleanup. Student organizing teams are brought in to the staff room at the end and complimented on their efforts, bringing the students to tears of gratitude. Teachers' lives are totally disrupted that weekend, leaving everyone to work 8am to 10pm and all they get for their thanks is a rice ball dinner. Yeehaw.
Am I focusing only on the negatives? Yes, for a reason.