a. The latest hot band is supposed to be coming to town next week.

Before publishing anything, I would do my best to find out directly from the band itself whether or not it is actually coming to town. Assuming they don’t get back to me within a reasonable amount of time, I would have no qualms with publishing this in my blog (provided I stress to readers that this is strictly a rumor and has not yet been confirmed). I obviously wouldn’t publish it if the band responded and confirmed that it was an untrue rumor.
My reasoning in this case is similar to the reasoning of the journalist in the textbook, Jason Foster. This is not a rumor with many extreme consequences.

b. The mayor is reported to be having an affair with his secretary.

I would not publish this story in a blog, and certainly not in a more professional, official publication. The consequences of this rumor are too broad and damning, and publishing them without any proof or official confirmation from parties involved is irresponsible.

c. The university’s starting quarterback is injured and can’t start.

I feel this one is similar to the first prompt, however, I would likely not publish anything until confirmation. Given that it is the local university’s quarterback, reaching out to him for comment is probably not difficult, and publishing the story without confirmation would be reckless. In the first prompt, the band is a more public and talked-about figure, and whether or not they come to town is a more fun topic to discuss casually on a blog. Whether or not the quarterback would be able to start has higher consequences and is more serious.

d. A local bank is about to close, and its accounts will be frozen.

I would not publish this until complete confirmation from the bank itself. Publishing this without confirmation could cause a panic, and we all know what happens when a bunch of people withdraw all their money from the bank at once.