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To get the list of all post type

get_post_types();

Output

Array
(
    [post] => post
    [page] => page
    [attachment] => attachment
    [revision] => revision
    [nav_menu_item] => nav_menu_item
    [readers-corners] => readers-corners
    [food-and-travel] => food-and-travel
    [music-entertainment] => music-entertainment
)

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To get the list of all custom post type (which is created by Custom Post UI Plugin)

print_r($options = get_option( 'cptui_post_types' ));

Output:

Array
(
    [readers-corners] => Array
        (
            [name] => readers-corners
            [label] => Readers Corners
            [singular_label] => Reader Corner
            [description] => 
            ......
            [supports] => Array
                (
                    [0] => title
                    [1] => editor
                    ......
                )

            [taxonomies] => Array
                (
                )

            [labels] => Array
                (
                    [menu_name] => Readers Corners
                    [all_items] => All Readers Corners
                    [add_new] => Add New
                    ......
                )

            [custom_supports] => 
        )

    [food-and-travel] => Array
        (
            [name] => food-and-travel
            [label] => Foods And Travels
            [singular_label] => Food And Travel
            [description] => 
            ......
            [supports] => Array
                (
                    [0] => title
                    ......
                )

            [taxonomies] => Array
                (
                    [0] => foods-and-travels-category
                )

            [labels] => Array
                (
                    [menu_name] => Foods And Travels
                    [all_items] => All Foods And Travels
                    ......
                )

            [custom_supports] => 
        )
)

>>>>>>>>>>>>>>>>
foreach ($options as $key => $value) {
    echo $value['label'];
    echo '<br/>';
}

Output:

Foods And Travels Category
Music Categories
Nation And World Category


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To get the list of taxonomy related to a post_type

$taxonomy_names = get_object_taxonomies('music-entertainment');
print_r($taxonomy_names);

Output:

Array
(
    [0] => music-categories
)


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--------------------------------------------------------

get all term list depending upon the taxonomy 

$taxonomies = array(
    'music-categories',
);

$args = array(
    'orderby' => 'name',
    'order' => 'ASC',
    'parent' => 26, // remove this line if you want to see all the list of term, use 0- for all top level or 

parent terms and give any term id to see there childs
    'hide_empty' => FALSE,
);


Output:

Array
(
    [0] => stdClass Object
        (
            [term_id] => 27
            [name] => Bengali
            [slug] => bengali-poem-of-the-week
            [term_group] => 0
            [term_taxonomy_id] => 27
            [taxonomy] => music-categories
            [description] => 
            [parent] => 26
            [count] => 1
        )

    [1] => stdClass Object
        (
            ......
        )

    [2] => stdClass Object
        (
            .....
        )

)