Yes, as I say, that error has been simply copied by one "tutorial" after another, and incorporated into the I²C backpacks since it "sort of" works so people think it is OK. But it makes contrast setting more difficult and wastes half a milliamp. That may not seem much to worry about except that the LCD itself uses less than a milliamp and this would be significant it operating from a battery. The backlight of course draws 20 mA.
Not really. You will note if you tried both ways, that the contrast control is much more flexible connected this way. Instead of working only over a very narrow range at one end, it works over a much wider range - at both ends. 
Speaking of confused people,
I don't suggest that. 
This is the equivalent of turning the potentiometer all the way to the ground end. In general, it will work and is OK to test if you are having problems (as you are), but generally does not provide the clearest display.
So you found that out. 
The contrast is indeed, not your present problem.
And indeed, if that is the display with no code running, the fact that you get only half a line of blocks demonstrates that the display is definitely faulty.
Interesting trick. Don't quite know how or why it does that, but again, the display is definitely faulty. You are getting only the right hand side.
So the verdict is a dead display. I was a bit puzzled with your original picture and thought you had a 2004 display but of course, it is a 1602. On a 2004, the uninitialised display is "blocks" on the first and third line.
So we can forget the contrast setting for the present. The display is unfortunately dead. 
Pardon us when we ask for your actual code, but we always want to check what is in your IDE, not what the tutorial said because - it isn't always the same. 
Not sure what you are trying to articulate there, but if you are talking about the resistor in series with pin 15, that is another story. It is unnecessary with AFAIK, all of the currently available 1602 and 2004 modules since "R8" on the back of the module is "101" or 100 Ohms.
Well, it always used to be, but on the one shown in #11, "R7" is now 330 Ohms so the external resistor is even less necessary. I can't quite see what "R8" is doing here, but it appears to add another 220 Ohms also. An extra resistor will not hurt things, it will just dim the backlight slightly and save some current. 