Newbie here! Is it possible to customize the “Links” “Categories”…

To edit Links heading you don’t have to edit any files.
Go into the administration section of your blog and click the “Links” Tab and then the “Link Categories” subtab. Click the “Edit” button on the row named “Links”. You’ll see a new screen with various options for that Link Category. Change its “Name” to “Favorite Links” and click “Save Category Settings” at the bottom of the Screen.

To change Categories heading, you have to edit one file.
In your index.php file find the part where it says

<li id="categories"><?php _e('Categories:'); ?> …

And change it to

<li id="categories"><?php _e('Slartibartfast'); ?> …

to make your categories heading read “Slartibartfast”, instead.