Hi.
Hmmm. There are a couple of ways to look at your situation.
The first is that you have to be really careful about internet safety. While there are many useful and informative things and people online, there are plenty of nasty, creepy, and just not good people and things there, too. It can be hard to tell the difference. The casting director you found may be totally honest and legit. Then again, he may not be. When chatting with anyone online, it's best NOT to give out any personal information that someone could use to track you down or harass you online. There are some basic tips about online safety that you might want to consider as well.
If you do chat or email with someone and make plans to meet, you should ALWAYS tell your parents and have an adult go with you. ALWAYS meet in a public place.
Why are you afraid to tell your parents about the casting director's email? It's good to have your parents' support when figuring out what you want to do with your life. In fact, telling them can let them know that you are serious about acting. Let them know why you went searching for casting directors, and why you thought this one sounded promising. Maybe your parents or another adult, like a teacher, could help you find references for the director to see if he is who he says he is.
It's great that you're researching the subject. You should get as involved as you can to make sure it's really the right thing for you. If you're not already doing it, consider auditioning for some school or community plays or taking drama classes.
Acting can be a tough field, so the more you know about it, the better.