I know the ingredients of drano- Sodium Hydroxide, Sodium
Hypochlorite, Sodium Silicate, and Surfacants, Contains no phosporus.
I wonder how do they work (how do they remove the clog, disolve hairs,
protein, cystein bond in hair, etc.) I know how the old drano (NaOH +
Al) worked. I want to know how the new drano gel work. Please tell me
your proposed (if not factual) chemical mechanism.
Any chemistry/organic chemistry major shall be able to answer this question easily.

I don't know about everything, but Sodium Hypochlorite is just a fancy
name for bleach, (a strong oxidizing agent) so that is fairly obvious.
 Also the surfactants are going to help dissolve any fats and greases
into water thus helping to remove any of those blockages.