I see in the right upper corner, that there are 10K pull ups on SDA and SCL. Or am I wrong? When using I2C devices with Arduino, all the people are screaming for pull-ups. So should I add pull ups for my SDA and SCL (where a pull up is on the sensor board) or not?
You really should and most I2C specs recommend 4.7k ohm pull-ups. The optimum value is based on the number and specific I2C chips being used on the bus, the physical length of the bus, and the clock rate being used. A O-scope is the best method to see the wave shape of the data and clock bits to determine the best value to use.
The reason many can get along without using any external pull-ups is because the AVR hardware has available and the arduino I2C library code enables internal 'weak pull-ups' on the SDA and SCL pins of around 40K to 50K ohms I believe. This usually works OK for a single I2C device mounted on a shield or with short wires. I know I have no trouble with a small 1307 RTC module that mounts right onto the shield connector that has no external pull-ups.
Lefty