Send e-mail without completing the form

You can use AJAX , which is a mixture of PHP and JQUERY .

Here's an example

$(".enviar_email").click(function(){ //botão para enviar
    var nome = $(this).attr("data-nome "); //variaveis
    var id = $(this).attr("data-id"); //variaveis
    $.ajax({
        type: "POST", //Pode usar, POST ou GET. Prefiro por POST
        url: "ajax/enviar_email.php", //ficheiro de envio de email com o código php nele
        data: "nome ="+nome +"&id="+id, //envio de variaveis pelo que você definiu no TYPE
        success: function(e){ //e equivale ao que retorna dele.
            console.log(e);
        }
    })
})

To send an email you will need to use php as already answered in this other question here: #

What do you mean by "Without finalizing the form"? If you want the person to come back later to fill out the rest of the form without having to re-enter the other information you can use html5 and the localstorage to do so by storing the information inside the user's browser. Follow link with explanations: link

If you want this information to be accessed from another browser or from another computer, you will need to store it in a database.