How to list the categories by custom taxonomy created?

You will want to use get_terms. The following code show you how to access the terms. Please see the Codex page for get_terms for more information about the args that you can send to the function. I also show all of the data that is returned in the array of objects.

// Set your args
$args = array(
    'hide_empty' => 0   // Show terms that are not associated with any posts
);

// Get the terms
$projects = get_terms('projects', $args);

// Loop through and use terms
foreach($projects as $project)
{
    echo 'Term ID ' . $project->term_id;
    echo 'Name: ' . $project->name;
    echo 'Slug: ' . $project->slug;
    echo 'Term Group ' . $project->term_group;
    echo 'Term Taxonomy ID: ' . $project->term_taxonomy_id;
    echo 'Taxonomy: ' . $project->taxonomy;
    echo 'Description ' . $project->description;
    echo 'Parent: ' . $project->parent;
    echo 'Count: ' . $project->count;
}