1. Choice a is correct.
The government approved a program that will give iPods to disadvantaged children.
That is a defining pronoun. No comma in the sentence? Use "that."
5. Choice a is correct.
The next topic he addressed was the many instances of identity theft.
The subject of the sentence always governs the number of the verb. In this sentence, "topic" is the subject. It is singular.
6. Choice b is correct.
The recent divestiture, combined with rising costs, is expected to affect profits.
Phrases are set off by commas -- you will never find the subject of a sentence in a phrase. In this sentence, divestiture is the subject of the sentence. It is singular.
7. Choice b is correct.
While answering the e-mail, I was interrupted by the phone ringing.
Keep related words together. If possible, modifiers should come next to the words they modify. Ask yourself "Who is answering the e-mail?"
8. Choice a is correct.
Unlike spam or spyware, spim is not under investigation by the federal government.
Keep related words together. The noun that heads the second clause must be the element that is being modified by the phrase in the first clause. Ask yourself, "What is like spam or spyware?"