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 don't need much current, you can maybe use an LED? A red LED has a voltage drop about 1.5V, which will drop your 3.3 down to 1.8V. It seems weird to use a diode or LED to regulate power, but this FPGA development board which I've used, the XSA-50: http://www.xess.com/shop/product/xsa-50/
(click on manual to see the schematic) uses a 1N4148 to do exactly that (derive 2.5V from 3.3V). Also, free power indicator LED for the 1.8V rail.
The correct thing to do usually would be to use a Zener, like this one from digikey. But I kind of like the LED idea better, and you might have one lying around.
Best Answer
The 60 % seems an unnecessarily severe requirement, given that mains voltage has a tolerance of only 10 %.
You can place the secondary windings in series instead of parallel, but the power supply will become very inefficient: 12.6 V AC rectified gives maximum 17.6 V DC, then the efficiency of a linear regulator is 3.3 V/ 17.6 V = 19 %. At 100 mA load the NCP1117 will dissipate 1.5 W.
If you do want to have 3.3 V in a relatively efficient way at a wide input voltage range you can use a switching power supply like this one by Recom. Input voltage range is 90 V to 277 V. This is for 1W or 2 W, but other modules with higher power outputs are available .