The maker is indeed Van Kempen & Begeer. Since this company started in 1961, the second mark has to be the sword for (small) silver after 1953. For further information see http://www.kempen-begeer.nl
Marks are indeed fake one's. This is typically a late-19th Century purse. These kinds of marks we also call Pseudo-marks, wich mean they are fake. One of the marks is meant to be the citymark of Groningen. .
It is Italian, Sicilian to be exactly, and made after 1947 (after Mussolini). The 3 is meant to be a maker's mark and the letters PA stand for Palermo.
This is a interesting box. It is a Scandinavian, most probably a North-German or Danish, socalled marriage box. They were made from the 18th to the late 19th Century. This is a 19th Century example. As far as I can see on the photo, the left mark is a maker's mark and the right photo is 12L. This is...