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.
It is highly doubtful if that supply has three separate outputs. Take an ohm meter and with the supply OFF measure resistance between each of the V+, V+ and V+ pins. I suspect that you will find them all bussed together.
Likewise use the ohm meter to measure resistance between the COM, COM and COM terminals. I suspect that you will find all three bussed together.
I give a strong indication of this being a single output supply because I zoomed in on the eBay picture that you pointed to and peeked through the screen cover. I could not see circuitry that would suggest a triple output unit.
Best Answer
Well the suitable way would be to have the PSU connected to the old DVD player innards so that its normal operational load could be running. You would then simply insert a current meter (DMM in current measure mode) in series with one output at a time and monitor the current consumption into the normal load. This will give a good picture of that that power supply was nomimally expected to deliver.
If the "old DVD player" is junked out and not available to be used for a nominal load then you have a harder job on your hands. One method to determine capability of the supply would be to put the thing on the test bench and connect resistor loads to the outputs. You want to utilize high wattage resistors for this so that they do not get hot and cause a change in the reistance of these load resistors. For this type of test you will need to simultaneously load all the outputs that you would like to use on the PSU. The idea is to start with relatively light loads and then interatively increase the loads to more and more current while monitoring the output voltage across each resistor and periodicaly checking the temperature of critical components on the PSU board. As you get to heavier loads it also pays to check each output with an oscilloscope to check each output for amount of noise and ripple.
When you reach load sizes that start to cause the PSU to get hotter than a nominal working value, increased ripple beyond more than 1 or 2% of the voltage levels of the output, or the nominal output voltage sags more than 4 to 5% then you know you are reaching the design limits of the power supply. From this check the current flow into each load resistor and you will have a close idea of the supply capacity.
For sustained usage of the supply it is recommemded to back off on the limits determined above. Also make sure to use the PSU in no worse enclosue space than it was in when in the DVD player. For exwmple if the original application had a fan blowing air over the PSU then make sure to provide as good or better environment in the re-use application.