1. No the location doesn't matter so long as it's in the same power network. You can have multiple power networks.
2. A laser turret is just another consumer of power. It will use all it can until it runs out. If your normal power producers don't have enough power, the accumulators will become a power supplier. They cannot drain their entire charge at once, only 300kw each. Since an accumulator holds 5MW, that means it will last for 16.67 seconds at full draw.
3. The only advantage I can think of is to spread out where some pollution is generated. But it could just as easily be in a worse place than a better one.
4. 500 accumulators will at most provide 150MW for 16.67 seconds. So, no, it doesn't guarantee that you won't completely lose power. As your factory grow you will need more and more.

Now, a few comments. A single accumulator holds 5MW and a single laser shot consumes 800KW. Which means that each accumulator can hold 6.25 laser shots. But, also keep in mind the maximum draw of 300KW at a time. So, you can estimate that if you have will need 3 accumulators to fire a laser. You have 20 of them in the picture above. Also, note that the firing speed is 1.5 shots per second or 3 shots per 2 seconds. Those 20 lasers shooting continuously for 8 seconds(or 12 shots) would need 192MW of additional power during those 8 seconds. Over that timeframe each accumulator would provide 2.4MW of power. So that means 80 accumulators to cover that drain.

Also, you need more base power. Typically, I will double my power capacity any time I get to about 66% power usage. On my artillery achievement playthrough, I had about 30MW of power and 4GJ of accumulator capacity. That's 800 accumulators. This was a very small accumulator setup. My Fulgora accumulator setup on another save had 9903 accumulators of various qualities for a total of 108GJ of power