But what is then y^2= x^3+7 needed for?

Are cofactor and order  used only for checking?

I understand '*' is this  http://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication operation.
And it is
X=Gx*priv mod p
Y=Gy*priv mod p

 ::)I understand this I meant * as sign of EC point multiplication.  
Is that right?

So all I need to do is
x=priv key*Gx mod p
y=priv key*Gy mod p

Is this right?

Indeed I don't care the formula will really help me

Please, don't blame me for being lazy, but I am not native english and mathematical notation of
x and y from those parameters and private key would really help me.

How can I count them from private key and Secp256k1 parameters. Can anybody give me mathematical notation for x and y?

Topic says it all.
I am mostly interested in peercoin, timekoin, novacoin and yacoin.