DM and CM noise filter
From what I know, a common-mode noise is a noise present in both lines
  with the same "polarity", while a differential-mode noise is a noise
  which is complementary in respect to the ground in the two lines.


Yes, that is correct but I would have said that a differential-mode noise is seen as an unwanted signal between the two wires of the differential pair.


  if I set the cutoff frequency of the two CM filters to a certain
  value, these two filters will just filter the signal within the range
  set. In the same way, the differential filter will just filter the
  input signal within the range set.


Absolutely and this can be a problem; if your unwanted signals are in the same part of the spectrum as your wanted signals then trying to filter-out the "unwanted" inevitably filters out the "wanted".


  How exactly this two filters works together?


They make an attempt to filter out noise that is significantly higher in the spectrum than your desired signal bandwidth.


  How can they act on different kind of noises if they are just LP
  filters?


They are just simple filters with simple mechanisms - they can't do magic and in many cases they fail to deliver but, on the other hand, in many situations they do a good job. Generally, filtering is not a great solution if the interference spectrum overlaps your signal spectrum.

On a side note, you might struggel to get the bandwidth you want from the chosen InAmp: -