1) I do not want to connect it on top of my arduino but with wires. This is because I want to have some switches in my arduino so I do not know where to connect them If I connect that on top.
Since you have the LCD shield already, you might as well use it as a shield, and there are two obvious options.
1. Connect your extra switches to the unused pins on the shield. The connection points are provided on the board for that purpose, the most obvious ones are A1 to A5 but D1 to D3 are likely candidates as well.
2. Have a prototype shied between the LCD and Arduino. This can take your switch connections etc., and provide mounts for items like a clock.
So using this diagram http://www.shieldlist.org/dfrobot/lcd
I conneected the bolds pins into the arduino equivalent pins. Plus I connected the GND,VIN,5V,3.3V of arduino to the lcd keypad.
But even if I run the example and I can identify button presses (not so accurate though) I see nothing on screen.
Should I connect them all?
2) I want to have a switch in arduino digital pin 11, so if i connect them all, where is that pin going to connect? And still a digital.read fro pin 11 will be enough?
I don't understand the problem. You obviously need to connect all the pins in order to do the job. If you have done that correctly and see nothing, it might simply be a matter of adjusting the contrast. Your board looks the same as mine, uses the same pins, and my buttons are on A0. If you must connect a switch to pin 11, which is not likely and probably a bad habit, then the proto board is a solution. I think a better solution is to put the switch on pin 3 instead.