For your first question, 'morphine by the clock' means a dose of medication that is administered through a machine on a regular basis - every half-hour, or hour, etc. There is no need for a doctor or a nurse to give the medication, only to decide on the amount and the frequency. They will monitor the results and adjust the dose as needed.
For your third question (I hope the above is OK for questions 1 and 2), 'fall apart' means to become emotionally unstable - to be unsure of what to do, how to do it, and to be too emotional to do anything worthwhile/profitable. As for 'the reverse is true', it means that the doctors do all they can and are unaffected by emotions and the situation - although people think that this a difficult time for the doctors and that their emotions may be too strong for them to do their job properly, they ignore their feelings and continue with the task at hand - with admirable results!
Hope this helps - and good luck.