Yes, the lowest aperture f-stop should be the one included in the name of the lens. A Nikkor 50mm f/1.8 has a maximum aperture of 1.8. Not that you should always use the widest aperture, but rather that it's available.
My arthritis is kicking in already, due to temperature dropping, so I have to keep this brief tonight.
Low apertures are good for letting in more light, but low apertures tend to lose some sharpness. Not "out of focus" sharpness, but simple clarity and definition. Prime lenses don't generally suffer this as much. And then certain zooms, like the Nikkor 80-200, are even somewhat immune, which is unusual for a zoom.
Generally speaking, you want to ideally shoot about two stops up from the minimum, for guaranteed sharp images. On the f/1.8 lens, for example, f/4 should be perfectly sharp.
The higher you go, the sharper it gets -- until you hit the point of diffraction. That's when the quality starts to go again. For most lenses, that happens after f/11. Many photographers consider f/8 the ideal sharpness depth, but it can vary on the lens. I have a lens that is perfect at f/7, or a third stop lower than f/8.
Now, if you want more depth, you require lower apertures, and possibly longer focal lengths. You may sacrifice some sharpness quality, but that's why you buy better quality glass!
Other times, you just want a good photo -- you don't get the luxury of perfect sharpness, excellent lighting, minimal grain, etc -- for example outdoor nighttime sports or indoor gym sports. ISO 3200-12800, f/2.8 and grain is to be expected.
Yes, in-camera flashes are relatively cheap and limited compared to "speedlight" hotshoe mounted dedicated flash packs. Of course, those cost a few hundred dollars. For example, the Nikon SB-600: http://www.amazon.com/gp/product/B00...SIN=B0002EMY9Y
Your observations on how settings affect one another are correct. Lower shutter means more blur. Higher ISO means more grain. Lower aperture means less depth of field.
The 50mm f/1.8 will give you very sharp images at most focal lengths, especially f/2.8 to f/8. Lower apertures will result in less depth, which can look like a "focus error" by is simply an issue of one object being in focus and the other one is outside the range where focus can be obtained.
To use an inaccurate example, pretend something is 10 feet away, and something else behind it is 15 feet away (5 more behind the 10). At f/8, let's say that both would be "in focus" because the depth of field allowed for anything within a 7-foot range to be in focus (the 10 and 15 are 5 feet apart, and both can be within the focal/depth range). Now at f/1.8, the focal range may be as small as 6 inches. You'll have to pick which item is in focus -- the 10ft or the 15ft distant object. And if you object is thicker than that 6 inches, parts of it might even be out of focus! Remember -- these were pretend numbers, to illustrate the point; I don't have time tonight to look up the actual calculations.
A 2x adapter absorbs two stops of light. In other words, a 50mm f/1.8 is equal to a 100mm f/4 lens. So it's only one stop better than the f/5.6 you're getting on that 18-105 f/3.5-5.6 lens @ 100mm.
The Nikkor 2x adapters are for specific lens models, such as the 80-200, 70-200 and 300mm lenses. So those are out. But "generic" third-party adapters can be pretty decent. I would go for the Kenko models, as Kenko is part of THK (Tokina, Hoya, Kenko). To retain autofocus on AF-S lenses, you'll need the higher-cost AF-S compatible model.
AF-S 2x ($225): http://www.amazon.com/gp/product/B00...SIN=B002C6QG4O
Non-AF-S 2x ($75): http://www.amazon.com/gp/product/B00...SIN=B000BX2QIA
The 50mm f/1.8 Nikkor in your link is an "AF" (not an "AF-S") lens, and can therefore work with the cheaper $75 adapter. However, the 2x will NOT work with your AF-S 18-105 lens. Not that you asked for it to work that way, but something to keep in mind.
You'll also note some negative reviews on the Amazon
site, regarding AF abilities with the cheaper $75 2x adapter. Those comments were left by morons -- their camera bodies only work with "G" type lenses, meaning AF-S/AF-I only. Your D7000 body works with older non-G "AF" lenses just fine. So disregard the negative comments. You can use this 2x and the 50mm AF without issue.
I sometimes carry a Nikon D200 in grip-less ode, with a 50mm f/1.8 and a 2x, and that's it. It fits in a tiny shoulder camera bag about the size of a large fannie pack. It's what I carry to conventions and trade shows, at the bottom of a larger "school" backpack (a leftover from college that once again has a purpose). So your plan is sound -- I do it!