I found these aging pages in the lid of a clarinet that came to me recently. They contain excellent advice about caring for a clarinet, and obviously from a teacher who had experience with students and the crazy things people do from time to time. I agree with almost all of his advice. You can download a printable copy below in the attachments.
#12. Rubber bands can eat the plating off of some kinds of keys.
#11. There are some careful things one can do to fix some problems. It's not hard to put in a pad temporarily, or use dental floss to fix a missing or broken tenon cork.
clarinetcloset.com, which has good illustrations. (I agree with everything on that page except using cork grease. One no longer needs grease if you have Valentino corks. See my advice on the Corks page.)
#3. Well you can't really “Squeeze” much moisture out. But I just pull the reed through my thumb and finger to get off excess moisture.
#4. I see quite a few mouthpieces that have been damaged by mouthpiece brushes. Don't use anything that will scratch or gouge the inside of the mouthpiece. You can more safely pull a nice soft handkerchief back and forth inside the mouthpiece to help in washing. Also don't use warm water. Warm water, if it is too warm, can turn your hard rubber mouthpiece an ugly drab olive color.
#5. I would say that oiling once every 4-5 months would be plenty for a new clarinet. After the first year, oiling once every 8-12 months is enough. Overdoing oiling can damage your clarinet. I would definitely oil the bore. It helps to keep moisture from making a b-line to some holes on the left hand joint (C#/G# especially). Not everyone agrees with me on oiling. (See my page on this.) I would go with your teacher's advice. Not the dealer's.
#6. Oiling keys every 6-12 months should be enough. Use some oil if you notice a key that doesn't operate smoothly.
#9. Yes, please!
#10. This point is true for real cord tenon joints. For Valentino corks, most of the time you just need to keep them clean.
#12. The corks and pads I use last so much longer these days! I would recommend a Spa Treatment once every two years, or sooner if the clarinet starts becoming hard to play. With the new pads and corks, complete repadding might almost never be required, EXCEPT if your clarinet is wooden. Then the benefit of having a spa treatment would mainly be to have the wood thoroughly oiled. However, if you are careful, oiling can be done yourself.