1. All of the class is/are here.
This is a SANAM pronoun; the noun in the "of" prepositional phrase determines whether the verb is singular or plural. "Class" is singular, so "is" is the right verb here.
2. Half of my family lives/live in Canada.
Works the same way as SANAM pronouns. "Family" is singular, so "lives" is the right verb here.
3. With a total population of less/fewer than two hundred and fewer breeding females
Drop the "and fewer": "With a total population of less/fewer than two hundred breeding females." Can you count the number of females? One female, two females, three females? Sure. So use "fewer."
4. More than 200 million people in world earn less/fewer than 10 dollars a day
This one's tricky. Are the people earning fewer than 10 "dollar bills" (not just dollars, but actual
bills)? No, we're talking about the amount of money in whatever form, not the literal number of dollar bills. The word / concept "money" is an uncountable noun (1 money, 2 moneys, 3 moneys? :) Use "less."
For a, b, c, d, e, not all of these are countable. When you're counting paper, do you say "1 paper, 2 papers, 3 papers?" No, you say "1 sheet of paper, 2 sheets, 3 sheets." Sheets are countable. Paper is not. (Unless you're talking about, say, complete papers you wrote for school - like a report. I wrote 1 paper, 2 papers, 3 papers this semester. That's countable.) (D) should be fewer because you can actually count the words; I know "less" sounds better to you, but that's because nobody actually says "fewer" any more. But we're all speaking incorrectly all the time. :)
On the others, what are you actually trying to say? If you're talking about the general concept of distance (b), the general concept of height (c), or the general concept of money (e), then they're uncountable (the nouns used here can function either as the literal, countable nouns, or as representations of the concepts). If you're literally talking about miles, feet, or dollar bills, then you're using countable nouns. Most of the time, for these kinds of sentences, we're referring to the concept, not the literal noun.