Yes, that is normal. It's called breakthrough bleeding and is caused by the fact you aren't pumping the hormones into yourself by taking the pill. Since most likely you will have to throw out your current pack and start a new one when you get back since you'll have missed a whole week, it will be considered your "period."
Well I am bleeding lightly. Is that normal? Will this be considered my period for this month, or will I have another one also?
You'll be fine it won't affect it. You can always call your doctor and have them send an emergency supply to a pharmacy near where you are
I would consult the pamphlet that comes with your pills for what to do if you missed a certain amount of pills in whichever week of pills this would be. Most likely, you'll have to start a new pack and use alternate protection for seven days, but I would check the insert. Definitely use protection if you have sex during this vacation. You may very well find yourself on your period during your vacation because of this.