You will often need to change your embrochure to get the high notes. Although some teachers would say it is bad technique to adjust your embouchure in order to voice certain notes, the altissimo range can be an exception, and often just a little more pressure is necessary, but without undue biting.
A good question, to which the answer might be yes and no. Harder reeds or wider tip opening on your mouthpiece may help get the notes, but very often at the expense of low notes. It stands to reason that you would not want to develop a good altissimo range, only to find that you can no longer play pianissimo low notes when required, or when you want to. In the short term if using a harder reed means you can get the high notes, it can actually be a good thing because you will get to "hear" the notes in your head, ie how they should sound before you play them. This is often referred to as "voicing". So it can be useful to use a slightly harder reed while learning to voice the altissimo notes, then revert to a softer reed once you feel confident about voicing the notes, and use your diaphragm and breath support to be able to articulate and sustain the notes. This way you will not sacrifice your low note.
