The terms furthermore and moreover are both transition words, meaning they help connect one idea to another. What's more, they both indicate something additional to what has already been stated. Moreover adds emphasis to the idea that came before it, usually introducing something particular or important (not an afterthought). But neither of these terms is commonly used in speech where shorter, less formal options do the trick.
To improve something is to make it more desirable in some way. To revamp something is to renovate, redo, or revise it. Revamp comes from the verb vamp, which in its earliest uses meant “to repair (a shoe or boot) with a new vamp.” The noun vamp here refers to the portion of a shoe or boot upper that covers the instep and toes. Revamp entered English with its own footprint, but the idea of making something old new remains central to its meaning.
The verbs explore and scrutinize both mean “to examine,” but scrutinize implies doing so with a more critical eye. To scrutinize something is to inspect it methodically with very close attention to detail. Items that are commonly scrutinized, such as budgets, data, and applications, tend to be complex and consequential. Similarly, people seeking positions of rank and consequence, such as candidates for political office, may be subjected to scrutiny.