Edit categories and tags in the WordPress front end

After much research problem solved! I'll post the solution to help anyone who wants to do the same thing.

Edit link on category page:

<?php
    $catID = get_queried_object()->term_id;
    //Obtem o ID da categoria visualisada.
?>

<form class="editar-categoria" action="<?php echo get_site_url(); ?>/editar-categoria/?editar-categoria=<?php echo $catID; ?>" method="post">
    <input type="hidden" name="editar-categoria" value="<?php echo $catID; ?>" />
    <input type="submit" value="Editar Categoria"/>
</form>             

Now the category editing page template:

<?php 
    /*Template Name: Page Template Editar Cetegoria*/
    get_header(); 
?>

<section class="conteudo-geral">
    <section class="conteudo" style="width: 990px" role="main">
        <?php
            $categoria_id = isset( $_GET['editar-categoria'] ) ? intval( $_GET['editar-categoria'] ) : 0;
            //pega o id da categoria da pagina anterior
            $terms = get_term_by('id', $categoria_id, 'category', 'ARRAY_A');
            //pega os dados da categoria

            if(isset($_POST['submit'])){

                $category_id = get_cat_ID($terms['name']);
                $category_link = get_category_link( $category_id );
                //pega o link da categoria para fazer redirecionamento da pagina no final   

                $term_name = $_POST['nome'];
                $term_description = $_POST['descricao'];
                //pega os dados dos campos de formulario

                $result = wp_update_term( $categoria_id, 'category', array(
                        'name' => $term_name,
                        'description' => $term_description ) );
                //função do wordpress para editar categoria

                if ( array_key_exists( 'term_id', $result ) ) {
                    echo true;
                } 
                else {
                    echo false;
                }

                wp_redirect( $category_link );
                exit;
            }
        ?>      

        <form action="" method="post">
            Nome da Categoria: 
            <br>
            <input type="text" name="nome" value="<?php echo get_cat_name($categoria_id); ?>" size="75" required/>
            <br>
            Descrição da Categoria:
            <br>                            
            <input type="text" name="descricao" value="<?php echo $terms['description']; ?>" size="75" required/>
            <br>
            <br>

            <!-- Caso precisar editar qualquer custom filed 
            Custom Field:
            <label for="category_custom_1order">Custom Field: </label>
            <br>
            <input name="category_custom_1order" id="category_custom_1order" type="text" value="<?php echo get_option( 'category_custom_1order_' . $categoria_id); ?>" /> -->

            <input type="submit" name="submit" value="Enviar" />
        </form>
    </section>
</secrion>

<?php get_footer(); ?>

The function you are looking for is wp_insert_term .

Comments:

• It's important to develop with error report on , you'd see that $pid = $_REQUEST [ 'pid' ]; gives a warning .
• Missing add a security check , otherwise any spam bot will abuse <form> .
• The form action has to point to the page itself.
• It's best to use custom fields names, so you do not run the risk of conflicts with names used by WordPress.

Here's a simple example, using a small part of the structure of this tutorial (worth checking the whole tuturial, note that it does not use nonce ):

<?php
/**
 * Template Name: Page Template Editar Categoria 
 */    
get_header() ?>
    <div id="container">
        <div id="content">
            <?php the_post() ?>
            <div id="post-<?php the_ID() ?>" class="post">
                <div class="entry-content"><?php
                    /**
                     * Verifica se o FORM foi enviado
                     */
                    if( isset( $_POST [ 'submitted' ] ) ) {
                        /**
                         * Verifica segurança
                         */
                        if( wp_verify_nonce( $_POST['nonce_form_sopt_28484'], 'nonce_form_sopt_28484' ) ) {
                            # FALTA conferir se a categoria existe
                            # FALTA definir se pode ser categorias-filhas 
                            $term_id = wp_insert_term(
                              $_POST [ 'nome' ], // the term 
                              'category', // the taxonomy
                              array(
                                'description'=> $_POST [ 'descricao' ]
                              )
                            );
                            if ( !is_wp_error( $term_id ) ) {
                                # DEBUG
                                printf( 
                                    'Categoria <strong>%s (%s)</strong> inserida com sucesso. IDs:<br /><pre><code>%s</code></pre>', 
                                    $_POST[ 'nome' ],
                                    $_POST[ 'descricao' ],
                                    print_r( $term_id, true ) 
                                );
                            } else {
                                # DEBUG
                                printf( 'Erro ao gravar:<pre><code>%s</code></pre>', print_r( $term_id, true ) );
                            }
                        }
                    } ?>      
                    <form action="<?php the_permalink(); ?>" method="post">
                    <?php wp_nonce_field( 'nonce_form_sopt_28484', 'nonce_form_sopt_28484' ); ?>
                    <input type="hidden" name="submitted" id="submitted" value="true" />
                    <p>
                        <label for="nome">Nome</label>
                        <input name="nome" id="nome" type="text" placeholder="O nome da categoria" size="40" aria-required="true">
                    </p>
                    <p>
                        <label for="descricao">Descrição</label>
                        <textarea name="descricao" id="descricao" rows="5" cols="50" class="large-text" placeholder="Descrição da categoria"></textarea>
                    </p>
                    <p class="submit">
                        <button type="submit">Criar categoria</button>
                    </p>
                    </form>
                </div><!-- .entry-content ->
            </div><!-- .post-->
        </div><!-- #content -->
    </div><!-- #container -->

<?php get_sidebar() ?>
<?php get_footer() ?>

  

Result: