1. Which Pioneer DVD burners come with NEC chips?
The IDE DVR-112 (and SATA DVR-212) burners are definitely NEC chipset drives. It wasn't for several more models before Pioneer swapped out to the non-NEC chips. Starting with the DVR-118 IDE / 218 SATA, Pioneer began to use chipsets from Mediatek.
These drives are maybe not as good as the classic NEC chipsets, but it's not necessarily horrible to have a Mediatek chipped burner. LiteOn has always made pretty decent drives (not the best, not the worst), and those have been based on Mediatek for quite a while now. Although I'd have to check some documents (so don't quote me on this), I believe some quite nice drives from Samsung and Optiarc also use Mediatek chips.
I'd still opt for a NEC-chip Pioneer, however, as first choice. It's the best, hands down.
2. How long will unburned DVDs stay good?
If you re-read that post, there was concern for discs that are already 6-7 years old maybe not being in the best condition in 3 more years. That would total 10 years as unburnt discs.
Buying a nice stock of blanks for yourself right now would easily last 3 years -- unless you're planning to store them in a garage, attic, freezer, or other insane climate that would damage them irreparably (burned or not) in that time span!
3. What's the best burning speed?
If you re-read that post carefully, it says "compared to the optimal speed (and rating) of the media" -- and you'll notice that "optimal speed" and "rating" are mentioned separately. It then goes on to discuss how rated speed is better than 1x, followed by mention of burning "a half or full step below that". The half or full step would be the "optimal" speed.
So ideally you'd want to burn 12x or 8x on those 16x discs, for the best burn quality. You're correct that a slightly slower burn (but not too slow) yields a better experience.
4. Why is my burned DVD still blank? Why doesn't the computer see my new burned DVD?
This is a common error because the drive is still locked. In order for a DVD burner to write to a disc, the drive must be locked from access by other processes. The problem with this is that the drive doesn't always unlock itself (or the OS doesn't see the unlock), and you get this unusual "missing disc syndrome" that's commonly complained about. It takes the computer a little while to come back to its senses. Generally, you'll need to shut down the burning software, and then unload/reload the DVD drive.
Engineers are not the most social people, and often live in a bubble. They have a hard time comprehending the world around them, even if they can dissect it into cute little math equations. DVD burners were created (as far as I can tell) with a goal of burning discs, ejecting, and burning the next one. It almost seems as if the engineers that designed much of the gear and process of DVD burning failed to comprehend that people would want to view their newly burned discs immediately -- without the undocumented task of closing software, refreshing the hardware, and waiting on the computer to "wake up" from its status. That's the only explanation I've ever been able to come up with, and I feel confident in it because several programmers and engineers have agreed with my statement.
.... Hope that clears everything up for you!