One way to tell whether the participle is dangling is to put the clause with the participle right after the subject of the sentence: "Bob's printer, rushing to finish the paper, broke" doesn't sound right.
Not all words in -ing are participles: in the sentence "Answering the questions in chapter four is your next assignment," the word answering functions as a noun, not a verb. (These nouns in -ing are called gerunds.)
For example: in the sentence "Since we've fallen a week behind, we'll skip the second paper," the first part -- "Since we've fallen a week behind" -- is dependent, because it can't be a sentence on its own. The second part -- "We'll skip the second paper" -- does just fine on its own; it's an independent clause. The independent clause can be a sentence without any help from the Since clause.
And it's not just a matter of high, middle, and low diction; there are many possible registers -- scientific, flowery, bureaucratic, vulgar. The important thing is to be consistent: if you jump at random between levels of diction, you're likely to confuse your audience. And that's a bad thing.
But although dictionaries are indispensable, you have to know how to use them. Be careful not to accord to them more authority than they claim for themselves: they're works of reference put together by people, not stone tablets engraved by God. The old argument that something is "not a word" because it doesn't appear in "the" dictionary (as if there were only one dictionary), for instance, is downright silly. Any pronounceable combination of letters to which someone assigns a meaning can be called a word; the question is whether it's a good word -- by which, of course, I mean an appropriate word. Many dictionaries list words like ain't or irregardless; that doesn't mean you can use them with impunity in formal writing. Pay close attention to the usage notes -- "Nonstandard," "Slang," "Vulgar" -- and be sure you choose the right word.
Dictionaries are also more concerned with denotations than connotations, and you're a fool if you think a dictionary entry amounts to a Get-out-of-Jail-Free card in any writing problem. Some dictionary may define gook as an Asian or queen as a gay man, but you can point to the dictionary all you like ("It's sense 3b!") without convincing anyone it's appropriate or inoffensive. Be sensitive to the associations your words carry to your audience.
Avoid, by the way, referring to "Webster's," which has no specific meaning -- any dictionary can use the name. Merriam-Webster, on the other hand, is a specific company that produces well-regarded dictionaries. Besides, dictionary definitions at the beginnings of papers rarely add anything to the discussion. A favorite line from The Simpsons, where Homer wins the First Annual Montgomery Burns Award for Outstanding Achievement in the Field of Excellence: "Webster's Dictionary defines 'excellence' as 'The quality or condition of being excellent.'"
Note that the phrase "different than" gets under many people's skin. In most cases, "different from" is a little more proper. So "Grunge is different from heavy metal" (but "Classical musicians play different instruments than jazz musicians do"). Brits sometimes use "different to," but that sounds odd to American ears. [Entry revised 6 September 1999]
"I took the paper" -- the paper is the direct object, because the verb took acts on the paper; the paper is the thing that was taken. "I called her this morning" -- her is the direct object, because the verb called acts on her; her is the person who was called.
"I gave him my suggestions" is a bit trickier. Here him is an indirect object, because him isn't the thing that was given; I gave suggestions, and I gave them to him. Suggestions is the direct object, him the indirect object.