An adverb that starts with e could be each or eagerly.
In fiction, you would like to give variety to your word choices. In formal business or academic writing, You want to prevent ambiguity and so may use the same word again and again to make your meaning clear. For example "contract" might be used repeatedly rather than along with some synonyms for it.
If this is true or false.. It's false. David Letterman is host of the TONIGHT show with David Letterman