Power Supply Design - Multiple Voltage Regulators
You haven't mentioned current output requirements but, the biggest problem you'll have is power dissipation and I'd urge you to consider using switching regulators for 12V, 9V, 5V and 3V3 and if necessary use them to generate 13V, 10V, 6V etc. and have Low-Drop-Out (LDO) linear regulators to take the drop to the final voltage you need.

The benefits are a significantly lower heat dissipation on the design and higher current outputs especially on 3V3 and 5V.

1) Regulators can be in series or parallel but it will be the 12V regulator that generates most of the heat if using linear regs in series. If using switchers then providing they can operate with an input at 24V+ then parallel is probably better BUT if you find a really decent 12V switcher and tee-off the other lower voltage switchers/LDOs from its output then this will work too.

2) I'd use switchers and linear LDO (optional)

3) I'd wire it in directly

4) I don't understand this point BUT neither do I see hanging a meter on the output as a problem.

5) Add fuses before the regulators if you must but it's likely that most regulators will have over-current protection easily added if not intrinsic to the device. I might be tempted to run the USB from its own 5V reg circuit. I might also be tempted to provide a -9V (or -12V or -5V) rail too.

EDIT - I'd probably put a LED on each output