1)Is the picture yu get with the preview the same quality than the final render (it looks like it to me)
2)Why I cannot seem to be able to launch a render (not a preview) of one frame and keep the picture on the screen ?It always disappear no matter what I do.
1.) Yes, the rendering you get in the renderregion is the same quality as the "real" renderer IF you use the same settings.
2.) XSI always closes the renderwindow when it finished rendering. If you want to view the picture after rendering is done you can either view the image in some imageviewer OR if you're using XSI 2.0.x you can load the default pass into the FX tree and then open the viewer and view it there.
if you want to render only ONE frame you can also do a preview and use the "save as ..." button in the top left of the preview window after you examined your picture ...