I think as of June 2020, it's still AES, as SM4 isn't registered in IANA formally backed by an RFC yet, and most browsers used by netizens in China are based on Chromium (some users use FireFox, and some government websites still requires IE!).
AES-CBC as implemented in TLS 1.2 is susceptible to Moxie Marlinspike's Cryptographic Doom Principle, which states:
If you have to perform any cryptographic operation before verifying the MAC on a message you’ve received, it will somehow inevitably lead to doom.
With the AES-CBC as implemented in TLS 1.2, an HMAC of the plaintext (and header information) ...
According to who? According to NCSC (the Dutch center for cyber security) for instance, TLS 1.2 is still considered "good", but it does go on to specify which cipher suites and specific configuration options are still considered "good".
This is kind of the problem with TLS 1.2: it has become a hodgepodge of different algorithms, key ...
Are their values fixed for each DHE group ?
Yes, by convention a named group includes at least $(g,\mathbb G,q)$ with $\mathbb G$ being a description of the group parameters (i.e. $(p,a,b)$ for prime elliptic curves or $p$ for FFDH), $g$ being the generator and $q$ being the generator's order.
How do the communicating parties using Finite Field DHE agree ...
The function to calculate a MAC takes a message and a key, and outputs a tag.
To verify a MAC, you want to take a message and a key, and output a boolean (true if verified, false if not) instead of a tag.
Thus, the two functions can't be the same, since they have two different type signatures. In C-like pseudocode
uint8_t* MAC(uint8_t key, uint8_t message...
Signing and signature verification are concepts related to public key cryptography.
In case of message authentication codes, there is a single secret key and one function:
T = MAC ( K, M )
T - tag
MAC - MAC function
K - secret key
M - message
Messages can be signed by either the client or the server and verified by the other, depending on the case. ...
Section 3 explains the data structures and their representation as octet strings (or byte strings: this RFC uses “octet” and “byte” interchangeably). See in particular §3.1:
Multiple-byte data items are concatenations of bytes, from left to right, from top to bottom.
An HkdfLabel is the concatenation of 2 bytes for length (big-endian, see §3.3), 7 to 255 ...