ETS provides at least 1 copy of an old chem GRE on their website (from like 10 yrs ago). Honestly reviewing your undergrad textbooks & notes is the best way to prep for subject GREs.
Honestly at that stage of your scholastic career - people don't tend to harp about age (I guess I would be curious if there was a 15 yr old kid in my cohort, but I wouldn't go out of my way to ostracize the person). Focus on making could networking connections and doing good research - that's what most people are in grad school to do anyhow.
I would agree with rising_star. What are your plans after getting your MS? If you plan on doing more schooling - the thesis option is better (also for industry).
Honestly, schools ranked that closely tend to have similar resources and produce pretty similar high caliber research. The things that separate the two are usually pretty minute and I would honestly go where you feel you would flourish the most (fit, environment, post-grad opportunities, etc.). Now the difference between 5th and 50th would certainly be much more pronounced.
Also I would suggest that you work on your writing a lot since that will be a filter that is used for international applicants in the engineering discipline.
You can ask them for an extension. However, I would advice against taking the position, getting the ball rolling, then screwing the department over by pulling out at the last moment. Will it be the end of the world? Of course not but you then screw over someone who would have committed to LSU all the way. Just my two cents and congrats on your acceptances.