Problem in a receiver circuit
I've just recently started studying RF circuit design, thereby my help might be of limited use. What we can infer from your problem description is essentially that connecting the mixer alters your gain; this makes sense as the latter is given by the gm times load product of the circuit. In your case the load is modified by the introduction of the common base stage of the mixer. This part essentially behaves as current follower (linearized by R19, but let's ignore that for the analysis), thereby your new gain is to expected to be somewhere around the gm of Q1 times the load of the mixer! As for the introduction of the undesired frequencies: I have to give that some more thought, without a rigorous mathematical approach I believe pinpointing the exact reason will be difficult.