«В» is used when you talk about games:
- Я игра́ю в ша́хматы. 'I play chess.'
- Ирла́ндцы игра́ют в хёрлинг. 'Irish people play hurling.'
- Я игра́ю в ку́клы. 'I play with my dolls.'
«На» is used when you talk about musical instruments:
- Окса́на игра́ет на банду́ре. 'Oksana plays bandura.'
- Я учу́сь игра́ть на синтеза́торе. 'I'm learning to play keyboard.'
- Она игра́ет на ци́не. 'She plays guqin.'
In French I learnt 'je joue au basket' but 'je joue du piano' because it is different for sports/games and musical instruments although в and на don't have the same meaning as à and de.
In English I think "we are playing basketball" automatically implies "together".
So, if this means "We are playing basketball together", how would you instead say "We are together playing basketball". For example, my mom calls me and wants to know if I'm with my brothers, so I want to emphasize I'm with them by answering "Yes, we're together playing basketball".
It can. Please report it if it's not accepted.