It's mostly a myth that it's much more efficient to power DC appliances like laptops on a full end-to-end DC system rather than using an inverter and then the existing AC-DC converter instead1.
Let's take a look at your first question:
1) How inefficient is it to boost 12V to 120V and then back to 12V as
in using a traditional car power inverter to power a laptop (i.e. the
12V car battery power is boosted to 120V by a power inverter and then
back to 12V by the laptop's power supply)?
It depends on your hardware, but it's not too terrible. You have two primary conversions: the DC -> AC conversion in the inverter and the AC -> DC conversion in the power supply for the appliance.
Most modern quality inverters are over 90% efficient and many approach 95% efficiency over a large part of their operating range. Very cheap or small inverters may be worse, perhaps in the low 80s and even good inverters are often less efficient when operating at very low power relative to their rated power.
For the AC -> DC side you'll find more variance. Some quality converters e.g., those supplied with some name-brand laptops approach 90% efficiency, but many others are in the 70% to 80% range. Very small AC -> DC converters, such as those found in USB plugs tend to be slightly less efficient than converters will fewer space constraints.
Overall then, you're looking at a best-case loss of perhaps 15% (a 95% efficient inverter with a 90% efficient power supply) to a worst-case loss with a reasonable inverter of perhaps 40% (an inverter in the high 80s combined with a 70% power supply2.
Now consider also that the "end-to-end" DC path will generally also need a DC-DC conversion unless the device happens to operate exactly at the voltage (say 12V or 24V) of your DC system. This conversion is likely to be, at best, as efficient as one of the above conversions. At worst, if you buy one of the various adjustable buck/boost converters with wide input and output ranges, the efficiency might be considerably lower if it is operating outside of its ideal range. So ignoring all the other factors, it is even possible that the full DC route is already less efficient than AC!
Still, let's assume that the full DC path is theoretically somewhat more efficient than the DC-AC-DC path, by perhaps 10%. Here are downsides of a full DC path that might outweigh that small advantage:
- Something like a home (or RV or whatever) as you mention in point (2) will already have existing 120V wiring: power appliances on a full DC system would require either locating those appliances very close to battery bank, or running a second DC wiring system at considerably effort (adding wiring to an existing house is a lot harder than doing it as it's being built - unless you don't mind ugly). Furthermore, you'll run into issues such as no standard outlet for DC power (the cigarette lighter is probably the closest widely supported thing, but unsuitable for many purposes).
- Lower voltages are inherently less efficient than higher voltages for transmission: both because a given absolute voltage drop represents a higher relative fraction of the total voltage, and because proportionally more current is needed to deliver the same power. This effect is roughly quadratic: a 12V system suffers approximately 100 times the voltage drop as wires of the same gauge at 120V of the same gauge to deliver the same power. An example: over 10 feet 14 AWG household wiring, for a load of 120W, a 120V system needs 1 amp and suffers a voltage drop of 0.042% - basically a rounding error. A 12V appliance of the same power would need 10 amps, and suffer a voltage drop of 4.2% - so over 10 feet of 14 AWG you've already lost about as much power as you'd lose in a good inverter. In a house, you could easily have wiring runs of 50 or 100 feet, resulting in DC voltage drops that make the system unsustainable - even with a small 120W load. In practice, you'd need to use a significantly larger gauge of wire to counteract this: a significant cost which could instead just be spent on more solar panels or batteries.
- AC is the default: almost every appliance you buy will by default come with an AC plug. There are all sorts of appliances where you can also buy a DC version, but often with a greatly reduced selections. Yes, you can buy a DC powered fridge, but you pretty much have to choose from the 1 or 2 weird models at your local solar/battery store. These are often twice the price of a fridge you'd buy anywhere else, and based on some old model that may inherently be less efficient. The same for DC powered fans, TVs, coffee makers, whatever. Yes, they exist, but the market is currently minuscule as the selection follows. You'll waste more money and be less happy with what you end up with than you'll ever save in "AC conversion losses". The one approach that does work here is getting things that run on AC but have an external AC-DC power brick: you can skip the brick and connect your DC system up directly (but again the voltages are usually weird things like 17V, 21V, etc, so you still end up needing a conversion).
So I'll be what seems like the lone voice here and say that any sort of large or medium sized "DC system" doesn't really make sense just to save on conversion losses when you are hooking up off-the-shelf appliances. 120V AC is actually a pretty reasonable method of power distribution, especially since it's the default input for almost everything you'd buy. The conversion losses are fairly small with modern equipment, and you usually can't avoid conversion losses entirely even with a full DC system.
1 I'll sometimes call this the DC-AC-DC approach.
2 Of course, you can push the worst case much further if you seek out a really inefficient inverter (but this is under your control) and find some device with a terrible (or just old) SMPS or linear regulator that is very inefficient.