My question is simple. How hard it would be to fabricate a Battery of customized shape say of 30cm x 30 cm x 0.5 cm that can be fabricated by DIY without requiring any specialized/ hazardous chemicals or manufacturing processes that can be easily fabricated in garage setup with upto 500mA operating current and capacity in mAH range upwards of hundred? Does anyone know any chemistry that can achieve this?
There are - or were - but this may not be the answer you want.
If you look at the September 1901 issue of "Model Engineer and Amateur Electrician" (now just "Model Engineer") you'll find full construction drawings for a 2-cell battery with (according to the article) a low internal resistance, using zinc and carbon electrodes, and "four ounces of chromic acid or bichromate of potash dissolved in 12ounces of water". All common materials, readily available from your local chemist (pharmacy) - at least, when it was written.
The battery had one interesting feature : to switch it on or off, you lowered the electrodes into the solution, or raised them.
To give some perspective, these instructions come from the heroic days of the magazine, when it was perfectly normal to build your own motorbike, casting and machining the engine's cylinder yourself.
This can be seen from the assembly instructions : "First well amalgamate the zincs by dipping them in dilute sulphuric acid, and then rubbing them over with mercury (use a piece of rag at the end of a stick for this)" - see the emphasis on safety here?
Lifetime? "If the lamp does not take more than 1/3 ampere, it should remain at full brilliancy for two hours right off", and "Renew solution when current weakens". (It's a primary cell, not rechargeable).
You would need to adapt this basic design to your form factor... though a slim tray full of LiPo cells is probably a lot easier.
You can build a "Gravity cell", a variant of the Daniell cell, whose constructional materials are zinc, zinc sulphate solution, copper, copper sulphate crystals and distilled water. Its limitations are that it must not be shaken and a current has to be continually drawn to keep the two solutions of different densities from mixing by diffusion. Your 0.5cm headroom can be enough for thin metal electrodes and two liquid layers. Expect about a volt output and a reasonable capacity that is easy to renew by replacing the consumed materials. See http://en.wikipedia.org/wiki/Daniel_cell (particularly the interesting way that experiments with Daniell cells lead to copper electrotyping).