Raspberry pi -Arduino bridge
1) How exactly do they work (connection wise)?


Physically they all sit on the GPIO sockets of the Pi, sitting on top of the pi. The Gertduino and AlaMode seem to have the same form factor as the Pi which makes them a little more appealing to me but I guess then is personal choice. 

Communication appears to differ but it will use Serial, SPI or I2C. I would imagine that you'd be able to choose an alternate one but not read enough about them to know for sure. Serial appears to be fairly simple, and it would be easy to debug, however you might struggle if you wanted to receive data on the Pi without the communication being initiated by the Pi.  I2C would overcome this as you can run it in multi-master mode. 


  2) is it possible to write one python code in the raspberry pi that
  when run can load the specific ino code into arduino?


As you can call external programs with python I would say that even if you have to resort to this mechanism then it would be possible. You can turn on the debugging in the Arduino IDE to see what it actually does, then either script it or make the calls from your python program. 


  3) which bridge would be the most suited for my project? (eg:
  Arduberry, alamode, gertduino, etc?)


I'd go for either the gertduino or alamode purely on looks particularly the matched form factor.