Well, it turns out that these aren’t rules at all! In fact, Mark Forsyth, the author of The Elements of Eloquence, calls the preposition rule “utter hogwash” and says that anyone who claims that you can’t end a sentence with a preposition should be told up to shut.
And, as for starting a sentence with “and”, linguist Neal Whitman tells us that this belief has neither historical nor grammatical foundation. In fact, he says, as much as 10 percent of the sentences in first-rate writing begin with conjunctions. (http://www.quickanddirtytips.com/education/grammar/can-i-start-a-sentence-with-a-conjunction)
Some people believe that starting a sentence with and or but turns the sentence into a fragment but actually that’s not true. Grammarians assert that starting a sentence with a coordinating conjunction (the famous FANBOYS – for, and, nor, but, or, yet, so) retains the grammatical integrity of the sentence.
And so what if it doesn’t? Does it really matter if every sentence isn’t complete with a subject and a verb? There’s an actual term – scesis onomaton – for a sentence that consists only of nouns and adjectives. And great literature, oratory and popular culture are full of them. Consider the opening of Dickens’s Bleak House: “London.” Or Star Trek: “Space: The Final Frontier.” And let’s not forget the classic “Finders keepers, losers weepers.”
So, go ahead! Use a preposition to end a sentence with. And start the occasional sentence with a conjunction. But not too many. Or it might get annoying to your reader. And that’s the last thing a writer wants.