Give yourself credit... IMO, anyone who goes through what it takes to get a PharmD (in IL, is TX similar ?) is NOT 'stupid'. And welcome, btw
You won't damage the car, per se, just using it in a less-than-optimally efficient manner w/ regard to FE. Since you're asking, that has to be your intention. Also, as Jason alluded to, you have less control of the car when you coast downhill in N - so that's why it's 'illegal' (in those places where it is).
You definitely want to leave the car in gear when descending hills in a hybrid - you'll get some regenerative charging from the car's engine & brakes (if you use them). W/o a hybrid system, I could understand if you were doing that previously, as you'd be effectively taking the engine down to 'idle', vs the increased RPM of descending in gear. For now, just take your foot off the pedal when descending - but for the future, take a look at what I describe next.
Your better bet to max your fuel economy is to learn / practice things like 'driving with load' - since I've started using this when I got my own HAH, I get a tank over tank avg of right around 30mpg, w/ almost zero highway. Best commute to work (22mi) was 37mpg, and my best highway was 39mpg for 50mi. Until this point, I had never achieved EPA marks in a car, much less exceeded them (29 / 37 is the EPA rating, as you may recall).
If you have the Navi in your car, there's a great tool in there - a real-time Fuel Economy Computer (otherwise known as a 'game gauge'). You access it via the 'Info' button on the right side of the screen, then selecting 'Trip Computer'. With this, learning the technique (as described in the Civic writeup that Jason mentioned) becomes a lot easier. But it can be done with any car, FE computer or not. You'll learn that easing up on the go pedal ever so slightly lets you maintain speed, but achieve up to 20% better FE.
Finally, your mileage will take a 2-3mpg jump once you hit between 1200 - 1700 total mi. That's when your initial 'break-in' has been achieved. You'll recognize other increases up to about 10,000 mi (when your engine s/b 'fully' broken-in) - but this first one will be the biggest and the one you'll notice easiest. You'll also notice the engine revs easier and doesn't seem as 'tight'.
Anyway, welcome again, and please consider adding your car to the mileage db - it's a good way for you to have your 'lifetime' FE tracked automatically, and for everyone else to see an additional data point for our model and compare metrics.
All the best,
) for the past 12 yrs and have been working on my doctorate for the past 3 which I am hoping to have completed by this summer - this car was my early "graduation" gift 
(because I'm in major burn-out mode 
)
