Do a GC or NMR of the sample to know its composition

Ok, thank you

Do you think if I increase the reaction time, will there be any effect or it remains same

It may change. Also vary the concentration of catalysts. Reaction temperature too.

I do not see how to form glycerol from reaction of (to) polystyrene. To have glycerol as a product is must have been part of the substrate or reagent. The yellowish tint is because of technical grade f either of the above, including the catalyst. What I see in the pic is a two phase system, probably the lower is the water phase, the upper the organic phase