Can someone which is not authorized be able to listen between the conversation of 2 clients and catch the key? Because if I understood correctly one client needs to send the key through a channel so the another client could decrypt the data... So yeah that's my question; Can someone not authorized in that time frame catch the key and then start decrypting any data that passes through that channel?
No. If you use an appropriate key exchange protocol, eavesdropping cannot allow an adversary to retrieve the key. For example, see the Diffie-Hellman key exchange.
In this answer I shall assume that the two relevant parties already share a strong symmetric key (ie not a password), which may have been established by e.g. using appropriate key agreement techniques (such as those used by TLS which may use asymmetric cryptography) or by e.g. physical, secure courier transport.
No, an attacker cannot learn the key or anything about the messages except their lengths if an appropriate (set of) encryption mechanism is used. In these protocols, the symmetric key is usually used to derive encryption and authentication keys and these are used to encrypt and authenticate messages between the parties. Man-in-the-middle attacks are then thwarted by the security of the symmetric-key encryption schemes as well as by the fact that the other party is authenticated by knowledge of the relevant symmetric key.
Additionally, sometimes the symmetric key is combined with the result of a run of the Diffie-Hellman protocol to gain extra security properties such as that when the symmetric key is leaked in the future, no past sessions can be decrypted.
One example set of protocols, that achieves these security properties given a shared symmetric key is the PSK ciphersuites from TLS.
The key needs to be established. When a key agreement protocol such as Diffie-Hellman (DH) is used then the same key (seed) is calculated on both sides, but the key is not send, not even encrypted.
If the key can be caught depends on the protocol.
With non-authenticated DH you might be tricked in establishing a key with an adversary. This is considered an active attack (so the attacker needs to be able to do more than just listen / eavesdrop). But it is an attack that doesn't even require an attacker to compromise the connection between the two parties.
In the end you cannot reliably send encrypted information to somebody that you cannot trust in some way or another.