[Cfrg] uniform random distribution in ECDH public key

[Robert Moskowitz <[e-mail]>]

I understand from RFC 6090 and 5869 that the secret key produced from an 
ECDH exchange is not uniformly randomly distributed and that is why we 
have the 'Extract' phase in HKDF.  Got that.

This question is about the public key, g^j:

I understand that like j, it must be a point on the curve, thus if the 
curve is p-256, both j and g^j are 256 bits long.  But is g^j uniformly 
randomly distributed like j is suppose to be?

Side question:  I am still unclear on the length of the exchanged secret 
(g^j)^k, is it 256 bits (for p-256) or larger (perhaps 512 bits)?

Thank you for helping me get all this straight.