1. How many times can i practically burn programs onto my flash memory on atmega8?
The data-sheet says 10,000 write/erase cycles.....but is it that i use only one cycle of the flash memory every time i erase or write a new program?
Yes, but it will possibly last longer than that (some may go sooner), although you probably won't ever get there.
Assuming an extremely extensive use, reprogramming the same chip ten times a day (each day) on average, would make it last for close to 3 years.
If you get to even halfthat number of read/writes, you're either obsessive or a real cheapskate
2. Does the size of the program count in the durability of the chips memory?
Not in a way that matters.
3. Does it have a mechanism that 'cycles' the memory locations used so that the memory wears out evenly, like in digicams and thumb drives?
Nope (and neither of my way too many cams and too many thumb drives have this functionality AFAIK).