"bolster" has 2 different meanings. In one meaning, it is stronger than support. If I say "the leaning wall was bolstered by a metal pole", if I remove the pole, the wall will definitely collapse. If I say "the leaning wall was supported by a metal pole", it means that if I remove the pole, the wall might remain standing, but will be weaker and more likely to fall in the future. That isn't the meaning that "bolster" has here. Here, it means "take something strong, and make it stronger." This meaning refers to "bolster rockets", which are smaller rockets you attach to a large rocket in order to allow it to go higher or carry heavier loads. "When I heard that Sally wanted to go whitewater rafting, I tried to stop her by telling her it was dangerous. However, that only *bolstered* her enthusiasm for the idea: "Great!" she said. "I've been bored lately, and a little danger is exactly what I need!"" For question number 1: no, you can't say "bolster". Neither of the 2 meanings fit. You could use "bolster" for either a better or a worse scenario. "Senegal was already one of the healthiest countries in Africa, and the new policy bolstered that health record, adding another 3 years to the average Senegalese life expectancy." "Lesotho's troubled healthcare system was on the edge of collapse, bolstered only by aid from South Africa. If that aid were removed, Lesotho would be forced to close most of its hospitals, and it would become an international health crisis." For question number 2: yes, it would be fine to say "support" here, but that would lead to 3 repetitions of the word "support" in a few sentences. Repetition usually sounds bad, so the author decided to use the rarer word "bolster" instead.

These are synonyms, but no two words or phrases portray exactly the same meaning. In this case, in one aspect, the word "bolster" suggests a stronger emphasis and carries the idea of public promotion.