All of the two-word compound modifiers of the four terms you presented need to be hyphenated. This is because the words in each of those word-pairs are not acting as individual modifiers but as a single adjective modifying the noun that follows them. In the interest of clarity, therefore, the four items you listed should all be written as follows:
1. street-dancing competition
2. public-speaking contest
3. much-awaited event
4. fund-raising activity
There really should be no cause for confusion when the compound modifier consists of a noun and a gerund. A gerund, after all, is a verb form that functions as a noun; indeed, in a word-pair like, say, “street dancing,” the word “dancing” is actually a gerund modified by the noun “street” functioning as an adjective. To make sure that this word-pair is clearly understood as acting as a single modifier of another noun, the convention in English is to hyphenate the word-pair, as in “street-dancing competition.” When the word-pair isn’t hyphenated in written form, as in “street dancing competition,” the modification becomes ambiguous. The word-pair “dancing competition” could conceivably be also understood as a compound term modified by the noun “street” acting as a adjective—a modification that gives rise to the absurd idea of “a dancing competition among streets.”
The two-word modifier in the term “much-awaited event” also needs to be hyphenated, but this time the reason for hyphenating is different—it is to make sure that the adverb “much” is clearly understood to be modifying the past participle “awaited” and not the compound term “awaited event.” We need to keep in mind that in such instances, the past participle functions as an adjective, and the convention in English is to hyphenate the pairing of such an adjective with an adverb right before it, as in “much-awaited event.” There’s an exception to this convention, though. When the adverb ends in “-ly,” like “keenly,” the hyphen becomes unnecessary, as in “keenly awaited event.”
For a more comprehensive discussion of hyphenation, click this link to
“Hyphenating for Clarity,” an essay of mine that I posted in the Forum in October of 2009.