As ruakh wrote, it's informal.

Is my previous sentence wrong? Must the real part be "really"?

This seems to be from American English so, the answer will depend on use. I have heard Americans use the word real, like this. It would not necessarily be wrong for someone speaking American English. The word should be "really", for people speaking the English kind of English.

Which version to use, will depend on which English you speak.

As ruakh wrote, it's informal.

Is my previous sentence wrong? Must the real part be "really"?

This seems to be from American English, so the answer will depend on use. I have heard Americans use the word real like this. It would not necessarily be wrong for someone speaking American English. The word should be "really" for people speaking the British kind of English.

Which version to use will depend on which English you speak.