hmmmm, interesting, I disagree with the other answers here . I think both "a hundred" and "one hundred" are perfectly acceptable in speech. They are certainly both in common usage where I live in the U.S.
So for the first question, I would say:
"a hundred bucks"= correct
"hundred bucks" (without a)= not correct
bonus option, also correct = "one hundred bucks"
As for the second question, it seems I was taught the exact opposite of the other people on this page. I was taught that formally speaking, you should not say "and" in a number unless you are talking about fractions or numbers after a decimal point. So according to the way I was taught, the best way to phrase the second sentence would be:
"I have a fever of a hundred three degrees." or "I have a fever of one hundred three degrees."
After a little bit of googling, it appears this may be a difference between American and British English, with Americans being less likely to use the "and" and Brits being more likely to use the "and."
That being said, even here in the U.S., you could also say "I have a fever of a hundred and three degrees" or "I have a fever of one hundred and three degrees," and almost nobody except the strictest grammarians would notice. So basically, (a), (b), and (d) would all be accepted usages here in the U.S.