Is it possible to resize image before saving it with media module?
First off, image dimensions are not the same as image sizes. Images could have the dimensions of 800x600 but still exceed 10 MB in size.

One possible solution is to create new image styles under /admin/config/media/image-styles/ providing your desired dimensions (e.g. 800x600). See attached image:



Then under the Manager Displays section of the Content Type containing the image field, choose the Image style you just created. See attached image:



Then set the Maximum upload size for your field in the Manage Fields section of the Content Type containing the image field. See attached image: