Here are the answers and further discussion.
1. The voltage across C1 is (approx) 1.414 * the AC secondary voltage. This is higher than the output voltage by enough to overcome the regulator's Vin-Vout limitation, for most instances. Your low-line performance may not be what you expect. Making C1 larger can help. The important thing is to ensure that when the circuit is driving its rated load, the lowest voltge across C1 is still above the Vin-Vout minimum. You need to look at the voltage with a scope to see the waveform.
2. Nothing here, but do take note, because the transformer current varies with the rectifier configuration.
3. If you raise the secondary voltage, there is more voltage across C1, but also more voltage across the regulator. The regulator has no choice but to turn it into heat, which you have to get rid of via a heat sink. If the regulator dissipation is low enough, then you get to omit the heat sink.
4. See #1.
5. The object here is to keep the ripple current from the transformer/rectifier/filter system confined to just that. Ripple currents can be high enough that the voltage drop caused by conductor resistance can affect things downstream.
6. nothing here
7. This should be obvious.
8. Nothing here.
9. You should put the finished supply on a Variac and vary the input voltage through the regulator's dropout point. Monitor the output voltage using a scope that is AC coupled so you can see any ripple getting thru. Put the supply on some sort of load. When the regulator operates below the Vin-Vout minimum, it goes in and out of regulation with every half-cycle of the AC line. The cleanliness of the regulator's output under these conditions is unspecified.
10. This is very important, and is the reason for making the transformer's secondary voltage AT LEAST equal to the desired DC output voltage. See #8.
11. The local bypass should be a capacitor with good HF characteristics, like a monolithic ceramic. 100nF is sufficient. It needs to be right at the regulator.
12. Refer to the regulator's data sheet for more detailed information.
13. Refer to the regulator's data sheet for more detailed information.
14. Refer to the regulator's data sheet for more detailed information.
15. P = E^2/R. The resistor should be rated at least 2x this amount.
16. Diodes are cheap. Regulators less so. Don't Muntz these out.
17. Refer to the regulator's data sheet for more detailed information.
18. If in doubt: make the heat sink bigger. You can use your handy digital thermometer (your thumb) to check the case temperature. If your thumb really doesn't want to be there, then you need more heat sink.