Is the order of elliptic curve the same as the order of point on it in finite field? The question is the same as: is elliptic curve cyclic? how to prove it?
update
Seems the above answer is no.
But I've a further question(maybe should post another thread?).
Is there a bounding for the order of a random point on an elliptic curve? Many zero knowledge algorithms choose a point randomly, I guess there should be a low limit ?

If you need to produce random points of large order, the standard approach is to use a fixed, known curve of prime order (which is then guaranteed to be cyclic), and choose random points on that curve.
Do not fix a point $P$ and then choose random integers $k$ and output $kP$, as suggested in one of the comments. This approach is insecure for many protocols.
A definitive resource for this topic is How to hash into elliptic curves by Icart, published in CRYPTO 2009.
