Are these 15 words legitimate or made up?

Here’s a list of words that have been under scrutiny in this approval process:

1. Administrate: A back-formation of administration and an unnecessary extension of administer

2. Commentate: A back-formation of commentator and an unnecessary extension of comment

3. Dimunition: Erroneous; the correct form is diminution (think of diminutive)

4. Exploitive: A younger, acceptable variant of exploitative

5. Firstly: As with secondly and thirdly, erroneous when enumerating points; use first and so on

6. Heighth: Rarely appears in print, but a frequent error in spoken discourse (Why isn’t height modeled on the form of depth, length, and width? Because it doesn’t shift in spelling and pronunciation from its associated term, tall, like the others, which are derived from deep, long, and wide, do. Neither do we say or write weighth.)