In a Server Key Exchange message, isn't it supposed to send both the public key's parameters which are for DH: the g(generator) and p(modulus), but the message only contains one public key called Pubkey: so is that the g, p or both, or is there a fixed variable like there is for the RSA public exponent which is 2^16+1? And where is g^e mod p?
From the screenshot:
EC Diffie-Hellman Server Params Curve Type: named_curve Named Curve: secp256r1 Pubkey: ... Signature: ...
This tells us the following: You used a key exchange with ECDHE. They key exchange used P-256 (the elliptic curve, aka secp256r1) and the given value describes the public ECDH key and the signature on this value.
The paramters you are looking for are hard-coded for P-256 and documented in several places (for example in this PDF). The $g^e\bmod p$ you're looking for is the Pubkey which is mentioned in the screenshot.