Image can be any size because they are going to be sized down by theme to fit content area. If images will not be big enough of course there will be white background on the sides, so It is better to create a bigger images that are going to be scaled down.
To add image under menu might be tricky but it really depends on where and how you want it to appear. Most likely you want to add it at the very end of
header.php file but it really depends on what you are trying to achieve.
If you don’t know how to add image using HTML you can use WordPress post/page editor to upload your image and then take its HTML code and past it where you want it to display.