I have the charger as in the attached photo (note: it has two USB ports and the current output changes depending on using one or two USB). Is it possible (without damages) to power one or two Arduino Yun with it?
Yep, it will work.
What are limits related to the input current for the Arduino Yun board?
Yun draws up to 315mA. See here: Arduino Yun, power draw - Arduino Yún - Arduino Forum
USB 2.0 is specified for up to 500 mA and Yun is released for being supplied using USB.
So no problems here because your adapter will support a minimum of 1,05A.