Is it proper to start a sentence with the word that ended the last sentence?

Answer 1

This is an issue of style more than it is of grammar. Usually, this tactic is used to provide emphasis of a certain point. For example, one might argue, “The point of the thing is to have sparkle. Sparkle draws attention like no other form of glitz.”

Remember that the key to good, impactful writing is the ability to change up sentence structure so words, phrases, and phrase patterns are not repetitive. You want to keep your readers engaged. So, using tactics like this are a nice touch as long as you do not over-rely on them.