I'm trying in vain to reproduce the following image. I tried all I know to maintain the straightness of the edges by applying a crease of 1 and by adding edges but as I apply a SubSurf it's a 'disaster' . Idealy I would like to have the edges not too sharp as we can see on the image. Thanks for you help.
This looks like the sort of thing that is best modeled using hard edge surface modelling, with manual placement of edges instead of using a subdivision surface modifier that will round everything off, then keep constantly fighting against it to try and keep sharp corners and tight edges.
Anyway, edge creases seem to work, all you need is an extra inset, then set edge crease to 1 on all corner diagonal edges.
Or alternatively you could instead use full control-edge-loops all around the sphere to keep smoothing from propagating too far.
Select the four edgeloops limiting the indented area and bevel them with the bevel tool Ctrl + B.
Select the relevant parts and extrude them inwards by vertex normal
Now add control edge loops with Ctrl + R around every sharp edge so smoothing won't propagate too far
Repeat for all necessary corners inside and outside where the edges must be sharp
Are you trying to copy the object in the picture, which is flat, or are your trying to create a square hole into a spherical/round object?
For a square into a sphere, the following method has the advantage of adding no edge loop around the sphere (which can mess up the topology) and no pinching on the corners: