You kept taking the pills so you're still protected. If you stopped taking them and didn't start again after the end of the placebo week then you would not be protected because the protection only lasts as long as you're either taking active pills or only having the number of placebo days that are in the pack.
Dont worry If you started your period then you shouldn't get pregnant but if you're really worried about it then speak to your doctor.
That's false. Depending on what pill you're on, it doesn't always work to skip. Also some women regardless of what pill they are on find that they still have bleeding when they try to skip. It's not guaranteed.
It has nothing to do with protection. The only way you mess up your protection factor is if you take less than the dose that you're supposed to take, such as missing active pills. But obviously taking active pills straight through would keep you protected because it's active.