Re: Can I change the padding on top and have the logo not stretched?
Is your site public so that it can be checked? It's hard to know what advice to give because the details differ depending on the theme and so on.
Images display at their original size unless they have height and width parameters. The logo image doesn't have these parameters set by default so I don't know where your logo is getting them from. Again, it would be good to see your site; more information is necessary.
-- Gary