Electronic – drive several LEDs using a Li-Ion charging chip

First, why would you do this? The 7805 will be perfectly fine with 12V. If you're passing a lot of current, use a heatsink. The diodes will only move power loss from the regulator to the diodes themselves.

1. In this case it should be fine, but diodes do not drop a fixed voltage; the voltage drop varies depending on current in a non-linear fashion.

   So for example getting 5V from a 12V source using 10 diodes in series would be bad, and the voltage could range from as much as 7V to as little as 2V, depending on the current draw. The 7805 has a minimum voltage of 7V to output 5V at 1 amp, so as long as you can guarantee this 7V you should be okay.

   Note that the output of the 7805 will vary depending on input voltage by a few millivolts - it will be slightly higher at 12V than at 7V.

2. The same loss happens no matter if you use resistors or diodes. The energy must go somewhere and it is converted into heat by either resistors or diodes.

3. The best practice here is just to feed 12V into the 7805. Introducing more components into the circuit will make for more chance of failure.

4. Why is a heatsink not practical? Here, I'm unsure if potting would work. Best to ask someone else.

You should be cautious when using the 7805 in an automotive circuit. The battery line is a harsh place. When you turn the headlamp(s) on your car/bike off, for example, the excess energy in the alternator has to go somewhere and it does - it appears as up to a 60V spike on the 12V line. And in some rare circumstances you can get a negative voltage on the battery line. Both of these situations will destroy a 7805, and the output could short, connecting the battery line to the 5V output, giving your load 12V instead of 5V.

The problem with everything that you have listed here is that your borderline to a full custom solution and you have left very little to compromise with. But i'll try to fill in all the blanks.

1. The PWM driver i would recommend is this one https://www.sparkfun.com/products/10615 It can support the voltage directly up to 17v. This would eliminate the need for opto couplers.

2. You want a N-Channel MOSFET and to switch it on the low side. N-Channels are cheaper and have lower ON resistance. Find one that can support the current and voltage that you need.

3. Don't use a capacitor. The capacitor looks like a short to the MOSFET when it's not charged. This can over current the MOSFET.

4. You are partially correct. The gate of the MOSFET looks like a capacitor. You will need a resistor in series with the gate to make sure you don't over current the driver. Beyond that as long as the gate can be pulled sufficiently high enough the current of the driver only effect the switching times.

5. Your math doesn't add up here. You state that each channel will draw 3A and at 27 channels you get roughly and hour of run time from the 100Ah battery. Using a boost converter may actually lessen that amount run time because there will be efficiency losses related to the converter. Also a converter that's capable of the kind of current that you want would be way over your budget. Run straight from the battery.