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Why do you want to reinforce these beams? Also, I am not sure that I understood your post well. You are referring to these beams as false beams. Why do you call them this? Regarding your idea to reinforce this concrete beam, just placing a steel beam under concrete beam will not transfer any shear from Concrete beam to Steel. The two beams act independently. However, the lateral resistance of frame will increase and that will result in your frame attracting more lateral seismic load than before as stiffness of frame will increase and stiffness attracts load... Doesn't look like a good idea. Do this if you can justify the retrofit and also if you can accurately quantify the effect.

Wsalaam Hashmi, The way I read it is that if you have already included the effects in your analysis. I believe ETABS has an option to apply Seismic force at eccentricity. I am a bit rusty on this. Thanks.

W.salaam Hashmi, For the check 2, your base shear is different and so is deflection. What is the basis of this check? Thanks.

The analysis is Linear. Automatic redistribution would have been possible if analysis were Non-Linear. In order to approximate redistribution (during cracking), the USER has to put some kind of stiffness modification. This applies to shear, torsion, moments, axial...everything.