I am now asking native (RP or Southern English) speakers or teachers.
What is the accurate position of the tip of the tongue in the case of the vowels (including diphthongs)? And in which vowels does the back of the tongue touche the palate? Thanks.
Obviously, I'm not an English native speaker but I feel qualified to answer your second question anyway. Let us start with the back vowel that is the closest one - with /u/. If we manage to prove that the tongue (its back because that's the highest part of the tongue in articulation of /u/) does not touch the palate, there will be no need to analyze the vowels that are more open.
If the tongue touches the soft palate it creates such an obstruction in the vocal tract that the resulting sound, though perhaps quite sonorant, could not be classified as a vowel. Also these pictures of cardinal vowels should show you that even the closest ones do not involve a contact of the tongue with the palate.
File:Cardinal vowels-Jones x-ray.jpg - Wikipedia, the free encyclopedia
File:Cardinal vowel tongue position-back(png).svg - Wikipedia, the free encyclopedia
In addition, the linked vowels are cardinals, i.e. when cardinal [u] does not involve a contact, English /u/ surely doesn't, since it is not as close as cardinal [u].