Hello. I will do Sentence 2 first. I hope this will help you better understand sentence 1.
Sentence 2 means "These stories were worth $400 million of advertizing that they didn't have to pay for.
Sentence 1 means "This publicity is worth many hundreds of millions of dollars of free advertizing." (In other words the person is getting (in this example expensive) publicity for free).
Sentence 3 means "He wanted to raise enough money to strategically advertize more than the competition". He is trying to "out-do" (do more than) his competition.
Raise does mean "collect" in a sense. It is usually used when someone is getting donations from other people--when a person is receiving money that other people give him. "Raise" doesn't always mean the money is given, but many times it is. For example, "Obama is trying to raise money from rich friends so he can become the president."