What is the best way for doing that? (PHP/CSS wise)
You want some code to be added to the
The code you need is simple, let's take the example you gave:
Of course, you would copy the image to your own server and change the path. You can check the styles used on the page, using a good web inspector/debugging tool (like Firebug).
With the theme you are using on your blog, there is no hook. So, I would recommend creating a Child Theme. The benefit is that your modifications will not be overwritten during a theme upgrade.
See the codex for details about the feeds URLs.
It depends. There is number of ways theme can be customized:
Most basic way to modify header is
But without seeing the internals the only person who can properly answer this is theme's developer.