Should the lump sum for the preparation (37.000 EUR) be calculated in the total maximum budget or on top of the total maximum budget? I.e if the maximum budget is 600.000 EUR do partners have 600.000 EUR + lump sum for the project preparation or the maximum budget of 600.000 EUR should also include the lump sum for the preparation?

Yes, the lump sum for the preparation costs must be calculated in the total maximum budget.