Using file management, we can upload images into Episerver.
Does it create images of different sizes of that image automatically in the Episerver itself once we upload? Or can we have a module written which integrates with file manager that performs the automatic resize and be placed in different folders of that website?
EPiServer CMS does not have the functionality you describe (though it supports resizing images inserted into the WYSIWYG editor). You might want to have a look at ImageVault.