Are the two connections of the Lan cable that come in the laptop and the Wi-Fi box always the same?
Clear xD
Yes, the cables / connections are standardized.
Yes
is always an RJ45 connector
Thank you. I didn't know because there are thousands of Wi-Fi boxes.
What do you mean by "same"?
OK
Not that I buy a cable and it doesn't fit because the box is too old.
And then Lankabel and ethernet Kabel is the same?
Network cables nowadays usually have The same plugs. What is decisive, however, is what speed the cable and the plug can possibly transmit. Normally it should be 1GBit today, but there are also 100Mbit cables. They will fit either way - only whether you get the maximum possible speed depends on which connections are specific and whether the cable fits.
Yes, it is the same ^^
And then Lankabel and ethernet Kabel is the same?
Jop, is the same
So I definitely want something faster than Wi-Fi because I want to gamble with it.
Each cable offers higher speeds than most WLANs. As I said, you should get one that supports the maximum speed of your connections. You can't tell which is because we do not know your connections.
One part of the cable has to go into the HDMI port on my laptop, right?
Yes.
For gaming and watching YOUTUBE, how do you find that: https://www.amazon.de/...07S6PM7R6/
Again: here nobody can judge what suits you because nobody knows your connections where you want to insert the cable. Therefore, the question can't be answered appropriately for you.