We would not usually use the verb "play" with the noun "English". Do you mean "practice" (AmE: practise)? Also, "shall we..." is very formal. If you're using italki, you could write, "What do you think about practicing English together?"

Yes.

yes to turn your phrase into interrogative. You say Shall we play English?. the other people except Jimmy have misunderstood and misread your question. They presumed incorrectly. And started a debate about whether you can Play English.

Do you mean, "Can we practice English together?"

In U.S. English, you would not say "Shall we play." You could say: Do you want to ...? Who wants to ...? These can be used when talking to an individual or a group.