In addition one question about how to read the rules when using the cantrips green flame blade or boom blade. Both cantrips state that a melde attack has to be made. In the PHB on page 205 it is written that a spell requiring an attack (melde or range) uses the spellcasting abilitiy modifier.
Does this mean that the bladesinger a) uses INT bonus when attacking with GFB or BB cantrips and when the bladesinger does b) a full attack (potentially with dual wielding) DEX bonus is applied?
if the answer is yes, is this reflected in the guide /statistics?
That would be the case, except the SCAG cantrips specifically state "make a melee attack with a weapon" as opposed to say Shocking Grasp which says "make a melee spell attack". The rules on 205 apply to spell attacks, while 194 outlines the rules for "melee attacks" and "ranged attacks".
The tables in the guide only reflect average damage output, not taking into account to-hit chance. However, all of the attacks in the tables (except Firebolt) will be Dex based attacks anyways.