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I personally play the 4 knights but have since realised many flaws with it. It has a very small win percentage in book openings explorer and seems to be quite a drawish opening. It is quite passive and doesn't activate bishops to good, open files. The ruy and Italian offer more variation and creates a more dynamic position and have more traps and leads to a more open game for both player. Practice has shown that white has an advantage in these openings.

As for your first diagram, I've seen this before and for white it creates the idea of a closed game and they want to place a knight on D5 and pawn on D3. I think black generally can reply with symmetry and play similar ideas.

 Hope this helps

The first position is incredibly solid and near impossible to break, if you want to slow the game to a crawl and go equal play e5, if you want to be dynamic maybe aim for d5 for some marcozy like position.

The four knights, eh, there really isn't any problem with it at all.  The only problem I ever see with it is the diffuculty in creating imbalences, well unless your opponent is going for a halloween gambit :).  With the italian, you have the moller, the evans gambit, or Ng5 vs the two knights.  With the scotch game, actually I have the same problem :P, but you do at least get a nice center which you don't get with the 4 knights (well, save the scotch 4 knights).  With the ruy lopez, you and black have such an assymetrical pawn structure that imbalences are a-plenty.

I don't know why anyone would get into the first position. If it started with e4 and was a Sicilian, then 2. c4 only makes sense to go to a Maroczy Bind kind of position...an acquired taste at best. If it started as a symmetrical English, e4 is too early, since it shuts down all other means to obtain a central break by leveraging e3/d4.

As for the 3/4 Knights setup: while solid, 3. Nc3  does not add pressure to the e-pawn or speed up White's development by making castling ready on move 4, like the Ruy or Italian. So it slows down the pace of development and puts all hopes for the initiative into the middlegame. It kind of lets Black off the hook for a move. 

I just picked up a lot of bits and pieces of theory since 1975 when I started playing in high school.

As for d4/e4, these are two completely different animals and neither one looks particularly "better" than the other. You have to ask what kind of game you want to play. The middlegame you get from one will be completely different from what you get from the other.

It all depends on your style of play. In the two examples you show (unless white plays something like the Halloween Gambit) the white player is going for a game in which there are high chances to get a draw. That being said, if black is considerably higher rated, this is probably the surest way in which white will lose the game. 

In the first example in particularly, I am happy to play with black against the Maroczy, so I would just play Nc6 followed by g6 and go for that. In the second example, I am not that familiar with the positions. I have played some of these variations for fun in the past, but in serious games I play the Ruy Lopez with white and the Sicilian with black.

You can't play for money on the internet.  It's too easy to cheat and use software analysis.