I agree with others that switchers are a better choice in terms of efficiency, but they can be somewhat complicated to deal with if you're inexperienced, and there can be lots of weird effects that aren't immediately obvious (precharge sinking, beat frequencies, etc.) that can make life difficult. Assuming you've figured out your power dissipation and know how much current each rail can deliver, if the linears will work for you, stick with them (at least for the first pass).
If you're trying to achieve a variable-amplitude square wave output on your adjustable rail, the chopping may introduce noise into the main 24V rail, which could show up on the other rails. You may want to have an LC filter between the main 24V rail and the regulator input to provide high-frequency isolation, and will probably need extra capacitance on the adjustable regulator output (bulk electrolytic as well as low-impedance ceramic) if you expect the square wave edges to be sharp.
1, 5) There are some dangers with your scheme.
Power dissipation in the linear regulators will be
\$(V_{out} - V_{in}) \cdot I_{out} \$
which is significant, especially for the lower output rails. 78xx-type regulators have built-in thermal protection around 125°C, and (without heatsinking) a junction-to-air thermal resistance of 65°C/W. Your thermal management will be challenging.
Another potential problem - if the series-pass element in any of your low-voltage regulators fails or gets bypassed (shorted), you'll present the full 24V input to the output. This could be catastrophic to low-voltage logic. You should protect your low-voltage rails with SCR crowbars that can sink enough current to put the DC/DC brick into current limit and collapse the 24V rail (they'll need big heatsinks too). Fuses are unlikely to be good protection since the 24V brick likely isn't stiff enough to generate the \$I^2 \cdot t\$ needed to blow a fuse.
2) Whatever floats your boat.
4) Meters aren't huge loads. Just use one of your rails.
3) Correct - all regulators have headroom requirements. If you want the maximum 24V out, you'll need a direct connection, and will have to rely on whatever intrinsic protections the brick will provide you.
You are wasting quite a bit of power by using linear regulators to drop 9 V to 5 V and particularly to 3.3 V. There is also no need to run the LED from 9 V. There is no such thing as a "9 V LED". There are some packaged devices that contain a LED and resistor so that the whole thing is intended to run from some particular volage, like 9 V, 12 V, 24 V, or whatever, but then you don't have just a LED anymore.
It would be useful to know the current requirements of the 5 V circuitry, the 3.3 V circuitry, and the LED. I'm guessing that the sensor probably doesn't take much current. In that case, I'd probably use a linear regulator to make 5 V as you suggest, but a switcher to make the 3.3 V from the 9 V. The sensor runs from 5 V and everything else, including the LED, runs from 3.3 V. That will be a lot more efficient. Assuming this is a normal red, yellow, or green LED, it can be run from 3.3 V easily with the right resistor in series.
Best Answer
Just a complement to what others have said.
What you say is very commonly done, with switching converters. I'd say that all modern motherboards include multiphase switching converters (usually, multiphase buck converters, with 3 or 4 phases), which imply exactly what you are asking about: connecting voltage regulators in parallel.
Let me explain the idea with one vs. three phases.
First, one phase. Imagine a (single-phase) synchronous buck converter, such as the one in the following figure.
You want to make Vo constant, regardless of Io and Vi (so, stabilize Vo). You need a feedback system. This system reads Vo, compares it against a target voltage, and uses the error voltage to increase or decrease a control signal, which is usually the duty cycle of a PWM signal. The signal PWM(t), together with its complementary (1-PWM(t)), are used to drive the controlled switches.
Let's say that the period of the PWM signals is T. Each period has ONE sample of the correction signal (the control signal), which is the duty cycle. In other words: during each period T, we can correct Vo only one time. Many things can happen to Vo inside that time interval. However, we can only apply one correction to it, per period.
Now, three phases. Imagine you have the three-phase synchronous buck converter shown in the following figure.
The goal is the same. You want to make Vo constant, regardless of Io and Vi. Again, you need a feedback system. Imagine that, similarly to the one-phase case, each individual buck converter is controlled by a PWM signal. However, the three PWM signals are not identical. They have independent duty cycles, and some fixed phase differences between them. For N phases, the phase difference between adjacent converters is \$\dfrac{360º}{N}\$. So, for three phases, the phase difference is 120º. The individual PWM signals "start" at different instants, inside period T, and each PWM signal has its own, independent, duty cycle. If we sample Vo at 3x the original rate, and make each one of those three duty cycles depend on a corresponding sample of Vo, we have not one, but three oportunities, to correct Vo, inside each time interval T. In other words. The three-phase synchronous buck converter can react three times faster to changes in Vo, Io and Vi. And it can do that using individual converters that are as "slow" as in the one-phase case! Equally slow transistors, and equally long time constants. Same switching frequencies, and therefore same (total) switching losses. So, that is one key advantage. Time of reaction is three times shorter.
Another key advantage involves the output (voltage and current) ripple. Whenever the N duty cycles are equal (or close) to 1/N, the output ripple is zero (or close to it)!! If that condition is satisfied, the sum of the three inductor currents is a flat constant, and therefore the output has zero ripple. If the converters are designed so that they will work in the neighborhood of those operating points, most of the time, the output will have a ripple much lower than in the one-phase case. Having a low output ripple means having less noise coupled to analog magnitudes and, generally speaking, being easier to satisfy tight ripple requirements.
For the same reason, current ripple through the input capacitor is also largely reduced. Close to those operating points, the input current, instead of being a pulse of width T/N, will be something close to a constant.
Of course, another advantage is that each individual converter has to carry only 1/3 of the output average current, but that is not because it is multiphase, but simply because it is "3 in parallel".
In summary, benefits of N-phase multiphase switching converters:
Time of reaction is N times shorter (faster), without needing a switching frequency N times higher (with the increase in switching losses that that would cause).
Output ripple may be close to zero.
Current ripple at the input capacitor is also largely reduced.
(Plus the benefits of having N switching converters in parallel).
Benefits of having N switching converters in parallel:
Parts in each individual converter need to carry 1/N of the current in the one-converter case.
Heat losses are spread across a larger area.
So, to answer your question: yes, some kinds of voltage regulators are indeed connected in parallel (and very commonly), so that we have all those benefits.
See also "Multiphase buck" section, in this page.