Hi Believer, whether you need 'a' or 'the' or neither often depends on context and the meaning you want to get across. You can't say that one option is always right or wrong.
1) In a case of mistaken identity (you are talking in a general sense about all cases of mistaken identity).
In the case of mistake identity (you are talking about a specific case of mistaken identity)
2) Abu is not his real name but it's the one he uses to disguise his identity. (This is the only fake name he uses).
Abu is not his real name, but it's one he uses to disguise his identity. (this may be the only fake name he uses, but probably it is one of several fake names he uses).
3) only if 'idea exchange' stands as an easily understood standard 'topic' for discussion (as in will be on fire safety). Otherwise if you are trying to describe the activity of exchanging ideas you need to say something like 'This week's meeting will be for the exchange of ideas' or 'We'll be exchanging ideas at this week's meeting'.