I would like to draw button in Illestrator and make it with several states (like normal, pressed, dimmed). Can I draw all this and them quickly switch between button states? Also I would like to export current active state to SVG etc.
Unless something has been added very recently, no, this isn't possible in Illustrator.
The best you could possibly do would be a collection of Symbols, then you can manually replace one symbol for another - scale and transformations would remain in tact. But this is far, far from anything dynamic.
InDesign does offer "states" for buttons. But whether or not Indesign is even feasible to use would depend upon the project.