There is a difference between a candidate that genuinely has varied interests and has not been laser locked in say wanting to be a doctor since the age of 10 vs. one that is obviously trying to game the system. In fact, more often than not, the strongest candidates have a healthy degree of curiosity and interest in a number of areas. The reason I ding'd the kids was not because they were trying to game the system, but because when we talked about a field that they had identified as being an area of interest, they failed miserably in demonstrating "intellectual strength and energy" in the topic, and when you stutter or ramble through a topic because you really are not familiar with it, it puts into question your "expressive abilities". The admissions officers that I have talked to have consistently said that the candidates who are successful among the many thousands who are academically qualified are the ones that tell a convincing story of who they are and how they will make the most of Yale and how they will contribute to Yale. To paraphrase a recent discussion, "We know who this kid is, all the pieces add up".
Waste of time, and you risk a lower score. Assume you got A's in English classes and will write good essays for your application. Those indicia's of writing ability matter way more than a timed test taken on 1 day.
@FtrEng42 given your son's accomplishments, I think he will plenty of great choices. The top 4 you listed are so disparate in geography, vibe (actually about everything). Has he ever considered and articulated what he wants out the next 4 years, academically, socially, life experience? MIT is a great (maybe it and Caltech are the best) school for kids that already know they love STEM and want to be surrounded by other STEM focused students. You won't get the big State U experience with the sports and wide range of activities (and students). If you haven't done so, maybe a good exercise to go through would be to go through a list of college attributes and determine which are important to begin to better focus your son's list.
If they don't ask for them, I would not pay the fees. If she has done well on the AP tests (4/5), I would self report those on the Common App (official scores don't need to be sent until the student matriculates and the school uses them for placement or credit). That will serve the same purpose for validating the grades on her transcript.
I normally believe that doing a lot of practice tests (whole and by section) along with using resources like Khan Academy and prep books (start with the College Board one) is sufficient. But here, since you have been out of school and you seem to be lost on certain types of math problems, you should consider a tutor if you can afford one (perhaps a local high school math teacher who is willing to help you at a reasonable hourly rate). A good tutor should be able to spot the types of problems and concepts that you are having difficulty with and address those with you specifically. If you want to increase your math score by 100-200 points, you have to be familiar with all concepts that will be tested. As @intparent points out, there are repeating types of problems (format and/or concept) and one of the keys to high scores is immediately identifying the "type" and then solving for the answer through the process you have developed for it. If you are consistently baffled by certain types of questions or concepts, you will not be able to raise your score to your targeted level.