what are the fundamental skills needed for a career in chemical engineering ?

Maths physics and chemistry. are needed.

The topic you will learn are material & energy balance,thermodynamic,fluid,heat and mass transfer,kinetic,reaction engg,process control,process design, economics,separation process.

Shamel, both of the previous answers are correct on the various courses that form the backbone of Chemical Engineering. Please understand that chemical engineering has broadened its scope of endeavor from chemical plant operations (which was mainly modeling heat, mass, and momentum transfer in chemical processes to sustain, optimize and improve operation) to include material science (polymer kinetics and properties), bio-engineering (using chemical engineering principles to model how the body functions) and industrial biosciences (fermentation, application of microbes to produce commercial materials) and other interdisciplinary sciences that impact anything from harnessing solar energy to the production of pharmaceuticals . Thus in addition to the core curriculum mentioned above one can specialize by taking courses more specific to what you envision your career direction to be. Make sure you search out universities that have accredited Chem Engr/Bioengineering. programs. There are many.

I agree with the Mr. Pandit that you need to take classes in math, physics, and chemistry (both organic and physical chemistry). There will also be specialized courses in chemical engineering, such as separation processes, reaction kinetics, transport phenomena, and process control. I also recommend taking some computer programming and at least a few basic economic classes to round out your education.

There are plenty of good colleges to consider, only you can decide which one is right for you.

Good luck.