Here is my opinion on this:
1. When smoke began to appear from Mount St. Helen, the authorities expected this dormant volcano to erupt, and ordered the evacuation of citizens to safety.
I`d say anticipated instead of expected. If you expect changes, you think they'll be coming soon; if you anticipate changes, you're preparing to deal with them.
2. The patient was very ill, and relatives were told that the doctors expected he would not live. The doctors could not anticipate ; they expected that the things might get worse. In my opinion expected is correctly used in this sentence.
Here is what I found while searching:
To expect….for many means to get the outcome that they “should” get
To anticipate… for many means to see the outcome that they “want” to get.
I am not sure that the above interpretation of the difference is entirely correct.
3. When the Senior Manager's position became vacant, Tom expected that he would be appointed, and was disappointed when a colleague was offered the job instead.- correctly used. Tom could not 100% foresee his appointment as a Senior Manager. He only expected to be appointed because he regarded it as likely to happen.
4. When he heard that his father was very ill, Paul anticipated that he might have to fly home to Australia in a hurry, so he packed a suitcase so that it was all ready, just in case his father's condition deteriorated.[/QUOTE]- correctly used. Paul realized that his father`s condition was getting worse and worse and his sixth sense told him that something bad was going to happen. Paul got ready to face the problem and tried to be prepared in dealing with it.
I am not sure if my thinking is correct. I expect some native speakers to correct me but I cannot anticipate anything.