While generating a random Elliptic curve what are the conditions i have to considerd? I want to generate a random elliptic curve over a prime field. What are the conditions I should satisfy?
For the NIST recommended standard ECC-224 bit curve with prime $p=2^{224}-2^{96}+1$, a reduction technique is given by $(z_1+z_2+z_3-z_4-z_5) 
\bmod{p}$, what is the logic behind in this?
Baring other requirements that you did not explain:

An elliptic curve can be written as $y^2=x^3+ax+b$. To generate a random curve over a prime field, choose $a,b$ at random from the prime field.