Preamble: I wrote this 7 years ago after I'd been rejected from Oxford myself. I had really struggled to vocalise my thoughts and feelings. I had quite an intense and stressful interview process where they kept me behind for days and days and it gave me a sense of (false) hope. I went to a Russell Group university for my BA and it was the happiest time of my life. I applied to Cambridge for my MPhil and, due to a number of factors, including COVID, had a really difficult year. I am now studying for my PhD in the US, and I can look back on my application experience with a much calmer and more measured mind (and perhaps a little bit of wisdom). My PMs are always open if you need to chat, and remember, whilst you might think of this as a defining moment in your life at this point, it absolutely will not define you in the long run.
Without further ado....
This feels a bit premature because I see a lot of people on TSR getting interview offers, which, may I congratulate you for, because that is an amazing achievement in itself.
But I do feel as though I for one never thought about rejection until it came, and hit me like a truck. I am extremely happy at my current university, but I'm still not over my Oxbridge rejection, and I'm not sure I ever will be. I was at interview for a long period of time, and they released the candidates one by one, with me being one of the very last, I believe the last for my course, to be sent home. Maybe they considered me until that moment. Who knows.
But the rejection was the first time in my life that one of my dreams, one that I'd had since I was about ten years old, had gone up in smoke. It made me feel like I wasn't good enough, academically, for anything. And as someone who was, and still is, considering academia as a career, this is pretty damming.
I didn't ignore the possibility of rejection due to arrogance, it was just something I never truly considered. I just imagined what it would be like to get in, not to not get in.
I considered reapplying but didn't want to spend a gap year possibly having to deal with rejection again. The course I am studying now is unique in module combination to me, something I could not have done at Oxbridge, or at any other university.
For interviews:
So whilst I really want you to enjoy the feeling of getting an interview, please keep the possibility in the back of your mind that you may end up at another university. And this is sometimes a better thing. I don't think I could have coped with the pressure of Oxbridge.
Enjoy your interview. If you're there for a few days, take some time to explore and relax. And if you've been rejected at this point, don't worry. It's not the end of the world.
For decisions:
Getting that letter or email may be one of the most exciting yet terrifying things in your life. Approach it how you like - open it instantly or leave it for while. Just remember, a piece of paper or an email doesn't define you. If you want to reapply, that's an option, and you will be a much stronger applicant the next time round. Going to a different university isn't going to be the end of the world. Just remember, you've made it this far. That's a massive achievement in itself. 
Update:
4 years later, I am now a postgraduate at Cambridge.
5 years later, I have a degree from Cambridge, and let me tell you that I had a much more positive time at my other university. Oxbridge really isn't the be all and end all.
7 years later, I am now happily pursuing a PhD in the United States.