i got a small slab to play with recently, and i was amazed at what it did. my hand got a "burnt" feeling after touching it for more than 3 seconds  

this is known as a cold burn. it's a common phenomena. items of extreme hotness/coldness can burn your skin.

i tried putting it in water in an enclosed bottle, and i saw rapid evolution of dense CO2 gas that filled the whole bottle very fast. why does such a thing happen?  

dry ice is solid carbon dioxide. the dry ice sublimed as it absorbed heat from the water. you observe dense carbon dioxide because carbon dioxide is a relatively 'heavy' gas compare to air. The rate of formation of gaseous CO2 by the sublimation is much slower than the the dissipation of carbon dioxide by convection current and diffusion.

also, i find it very brittle. what gives dry ice this property?

imagine what happens when you try to displace layers of carbon dioxide inside dry ice. hint: similar reasoning why ionic solids are brittle

last of all, is there anything wrong with drinking the water after dry ice has "dissolved" in it? because i did so, and it tasted plain and fizzy felt a few burps after that.

LOL. you are just drinking carbonated water.