Hello, Sergev!
Thank you for your question!
The line you mentioned is not very popular because white gets comfortable edge without much efforts.
Your 1st chapter (6.e4 Nxc3 7.bxc3 cxd4 8.cxd4 Bb4+ 9.Bd2 Bxd2+ 10.Qxd2 0-0 11.Bc4 Nc6 12.0-0) is the line white usually gladly follows being faced this opening. However, then he could find that the real work it required to increase or even to maintain the advantage, which has been obtained so easily.
Your 3rd chapter also gives a stable advantage for white but your selection of the lines looks rather incomplete – many top players were happy to pressurize black’s position after 6. g3 Nc6 7. Bg2 – such as Kramnik, Anand, Karpov, Ivanchuk and others. However, it must be mentioned that this position more often originates from 1. Nf3 and then there are some possible move orders, for example: 1. ..c5 2. c4 Nf6 3. Nc3 Nc6 4. g3 d5 5. d4 e6 6. cd5 Nd5 7. Bg2 etc.
So I think it is not a big surprise black usually prefers more solid opening lines, such as 4. …Be7, in which white’s task to get and then to maintain the advantage is more difficult.
In conclusion I would like to say that there is no need to give here so many lines copied from CB database without any comments – then it’s not so easy to understand which line is supposed to be important and for what reason. I always check my database but, of course, if you believe you have found really important theoretical game which cannot be found in the well-known sources – you are very welcome to share your ideas.
Good luck!
Ruslan