Boost PWM Signal to 12 V LED strip

The 1.5V seen on DIN is probably just the level the input floats at with nothing connected.

This can be checked by placing a large value resistor, say 10K etc, between the input and ground. The resistor should pull the input low and the pin should read 0V.

On some occasions it may happen that a circuit's pin is being driven at a certain voltage. If you connected it to an output on an Arduino that was at Vcc or GND, it will short and may damage the Arduino due to the excess current. This can be seen in the design of Arduino boards with FTDI USB to Serial chips. The FTDI TX pin is driven high when USB is connected, however, if a user set the Arduino RX pin to output low, there would be damaging current flow. So they put a 1K resistor in between the two pins to limit the current if this happens.

The same thing can be done in the above circuit where it is not known whether the pin is being driven or not. The resistor will limit the current if it is, preventing damage.

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.