I'm using jquery validation plugin at my contact form, which returns if something is wrong in the form, but even if the entries are incorrect (for ex. name not longer than 1 character) I can submit the form and it sends the email with the incorrect data. How could I prevent the button from being active before the entries would be all correct?

$(document).ready(function() {
    var newHTML = '<div class="col-sm-12 text-center" style="color:white; background-color:#6f8595; padding-bottom:15px; border-radius:5px;"><h3>Thank you for your message!<br />We will get back to you as soon as possible!</h3></div>';

    $('#myform').validate();

    $('.btn').click(function(){
        var data = $("#myform").serialize();
        $('.form').html('').append(newHTML);
        $.post( "includes/sendmail.php", {data});
    });
});

Like this:

$(function() {
  var newHTML = '<div class="col-sm-12 text-center" style="color:white; background-color:#6f8595; padding-bottom:15px; border-radius:5px;"><h3>Thank you for your message!<br />We will get back to you as soon as possible!</h3></div>';
  $('#myform').validate();
  $('#myform').on("submit",function(e){
    e.preventDefault();
    if ($(this).valid()) {
      var data = $(this).serialize();
      $(this).html(newHTML);
      $.post( "includes/sendmail.php", {data});
    }
  });
});

Alternatively according to documentation you can execute the AJAX call in the validation submit handler - something like this:

 $('#myform').validate({
   submitHandler: function(form) {
     var data = $(form).serialize();
     $(form).html(newHTML);
     $.post( "includes/sendmail.php", {data});
     return false;
   }
 });

more