It's a special technique called altissimo. This upper range can be hit a variety of ways. There are trick fingerings, overtones, simply overblowing regular notes, etc. There isn't a special mouthpiece, though you could say some higher quality mouthpieces better facilitate the altissimo range. I would advise getting a book with all of the fingerings, it would take ages to put them all on here for you. Though if you have a specific note you would like to know, feel free to ask and I'll post it for you. You should only approach this once you're totally comfortable with the rest of your horn, and have a well developed eoumbechre. Doing this wrong(bitting down or pushing on the reed, or changing your eoumbechre) can be very detrimental to your playing. No question is stupid, we all have to learn things one way or another.

I don't think it's a special technique, rather a harmonic scale. About 40 years ago i bought Ted Nash's studies in high harmonics. and I recommend that book. At the back of book, there are some great solos. Some of you kids are Charlie Parker fans, and the book has Salt Peanuts, a song played by Diz and Bird. Where did they come up with the name altissimo? I guess it's politically correct. It reminds me of used car. Nowadays the cars are pre-owned. You have mess with your mouthpiece and reeds a little bit if you really want to climb on the top of the horn. Don't worry about your embouchure too much , as long as you hit the notes. People are talking about their throat and their ears and making it too hard. On the other hand, you don't want to get hung up on the harmonics and high notes. A good example of that is Arturo Sanchez. He is arguably one of the best trumpet players in the world, but he gets carried away in the high register. What you don't play is as important as what you play. If the fingerings in the book don't work, just use trial and error until you find what works. Tear it up :)

Yes, he was right by calling it the altissimo. On both the alto sax and the tenor I've gone up to a quadruple D. All you have to press is the first finger used for that F you were talking about. It worked for me at least.