If X, then Y.
Use the present for X if the fact seems possible, from your point of view or from that of the subject of the clause.
Use the subjunctive for X if the fact is very unlikely or not possible (eg. If I were you).
As for Y, it must be in agreement with X from a tense point of view. (2) is clearly incorrect as "If I am you" is impossible, and the tense in "I'd tell him the truth" doesn't fit with the present in the preceding clause.
(3) is correct because the subject may truly believe he's a professional singer. Then, the second clause "I'm Pavarotti" must be in a matching tense, that is, the present (note that you can have other tenses depending on what you want to say, Cf. mixed conditional on this site -- but here the present is clear).
Don't mix up the two clauses X and Y: that's the difference between (2) and (3).
FRC