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.
If you take the input for the 7805 from the 7809 output, you must include the current drawn from the 7805 into account when determining the power dissipation in the 7809.
You should not use a voltage divider to make 3.3 volts - the voltage on your 3.3 volt line will vary depending on the current drawn from the 3.3 volt line, as that current will have to flow through the "top" resistor of the divider, increasing the voltage drop across it. Look for a dedicated 3.3 volt regulator, or use an LM317 or similar adjustable regulator.
Depending on the currents you need from each supply, it may be best to use a switching regulator to get from the 15 volt supply to 5 volts.
Make sure you have adequate heatsinks on the linear regulators!!
Best Answer
From what you're saying, it sounds like you want to do this from ac wall power? Please clarify. Although you say you want to use a linear voltage regulator, I would caution against that. It may be better to combine a transformer, a full bridge rectifier, and a switching power buck (or boost) power supply that meets your quality requirements.
Linear voltage regulators will have ripple, and because many things don't use them anymore, they aren't subject to the kind of innovation that switching supplies get. Linear power supplies remove power as heat. This can be calculated by the equation (Vin - Vout) * I = Heat (in Watts). It is because of this wasted power that most higher voltage things don't use linear supplies. Of course, arduino boards use them because the draw very low current, and it much less space consuming.
If your goal is less supplying power and more a precise voltage, consider a precision voltage reference. These can be as cheap as $5 if you're willing to buy from china.
In conclusion:
Linear power supplies step down voltage with considerable ripple based on many factors, like supply voltage, and also produce heat
This heat makes them a poor choice for situations requiring high voltage, long battery life, or both.
A switch mode power supply may be good if you can find one with that precision if you still want efficiency
Also, consider a precision voltage reference if you need very high precision.