Is My Height Normal For My Age?

I will be 15 years old on August the 31st and my current height is 5'5 (actually I am like 5'4.9, but I am missing less than the half of a cm for 5'5, so I am technically 5'5). I am about, 5'5 1/2 or 5'6 with my shoes on. Most of my friends are real tall for their ages, (5'7+) except for 1 which is shorter than me, but the difference is hardly noticeable. I wish I was taller...

When I become a adult, I hope I will be 5'10 (my dream height because is the average, cause I know I won't be tall). Please tell me this is normal for my age, or that I am going to grow (only if it's true, please be totally honest). My mom is 5'1 and my dad is 5'7, but the mom of my mom (my grandma) was 6'0 or even taller, is there a chance I could have inherited her genes (which I doubt because I don't look nothing alike to my mom)? Please answer this questions:

-Is this height normal for my age?
-Will I reach 5'10? My step dad says I will... (Please don't bullshit me saying stuff like "Idk nature always have its mysteries or **** like that").
-Is it possible that I got my Grandma's genes? I have a friend that has shorter parents than me, and is 15 years old and 5'10!
-This is probably the most important question, can I start lifting weights? Actually I already started, like 2 weeks (almost nothing) with 10 - 15 pounds, also abs exercises... I don't know who to believe, my mom says if I do weights I'll stay midget like her, and my dad says I will keep growing normally, to 5'9 at least. What do you say? Yes or no?

Thanks, for taking time out of your lives for reading this and commenting, a million thanks to you and your ancestors! Remember, please be honest, hate it when people lies to me just to make me feel better!
Oh yea, and I forgot to add that I weight 120 pounds (last time I weight myself, I should weigh more by now, about 1-3 pounds more at least).

I almost forgot, to ask you if swimming could stretch me, so I could look taller? Not only swimming, but other stretch exercises?

I know that lifting weights doesn't affect my height in any positive way, what I am concerned about is if gets affected in a negative way, like by stunting my growth, I ask this because I have heard a lot of people say that lifting weights will stunt your growth. I just want to start building some muscle, so that when I am around my 18's I will be ripped ;D