In the United States, when we are talking about U.S. stocks, we usually say "the stock market." There are about twenty different stock exchanges but electronic trading is so fast that we consider them to be a single market.
People sometimes say "the markets" or "the capital markets" or "the financial markets" and that includes stocks, bonds, commodities, and other things.
If we are talking globally about the stock market of more than one country, we would use the plural: "European markets were down yesterday," "Emerging markets did well in 2000-2009 when the U.S. market was lagging."
We say "bull market" if we are talking about one historic period--"the great bull market of the 1990s."
We use the plural if we are talking about more than one: "According to this chart, there have been twelve bull markets since 1926."
3) is perfectly clear, correct English, but it isn't idiomatic. A low point in stock prices is called "a bottom." I think "periodically" suggests more predictability than is the case.
"The stock market hits bottoms from time to time."
(They probably do NOT say it this way in British English, because "bottom" is too closely associated with part of the body).
4) isn't correct English; it should be
"Fast increases and decreases are dangerous," or
"Rapid rates of increase and decrease are dangerous."
A more idiomatic wording would be:
"Sharp price movements are dangerous."