Electrical – External power supply design (12V to 5V and 3.3V) for arduino based system

The problem is, all the modules I've looked at have a maximum supply limit of about 14.5V and worse, their sound quality starts to diminish at about 10.5V.

A good 3S Lipo has a usable range of 10.5-12.6V when discharged at a reasonable rate (1C or lower), so it should suit your application perfectly. 9.6V is into the over-discharge zone, where the battery has no capacity left. You should never let the voltage drop below 10.5V under load (11V resting).

So with this choice, the sound will begin to suffer long before the pack has exhausted its useful charge.

If the amp sounds good above 10.5V then by the time you notice the sound quality degrading the battery is already over-discharged and will die very soon. You should use an under-voltage alarm and/or cutoff device to prevent the battery voltage from going below 10.5V.

The first thing you ought to do is get the local/state/national regulatory standard for electrical wiring. In the US, for example, the starting point would be NFPA 70 (the National Electric Code) which you can access electronically for free through the NFPA's website. Usually the requirements near water are different than those in dry areas, for obvious reasons you already are aware of. The standards will help you better understand the safety ramifications that you're rightfully concerned about. Note that local laws (like permitting requirements by a township) may also require you to have an electrician and/or engineer approve the design and/or perform the installation.

In particular I'd like to point out a potential misconception about using low-voltage here: even a converter to low voltage is not necessarily considered "safe" unless there is enough isolation between the high and low sides; too little and it is easy for a fault to dump line voltage on what you think is just 12V. These kinds of converters will explicitly note that they are qualified as something like "PELV" (protected extra low voltage) or "SELV" (safety extra low voltage). The use of a GFCI may or may not be sufficient to cover safety concerns, check the safety standards that apply to your location.

Also make sure the jacketing/insulation/filler in your wiring is rated for outdoor use, particularly in regard to moisture but also the potential for impact/abrasion, because anything else is is a recipe for an electrical fire (again, the relevant safety standard for your area will help you determine the exact requirements).

To get into some of the non-safety aspects of your questions:

Voltage drop: yes, this is a concern. Recall that wires aren't perfect conductors, they have some resistance per unit length, which causes a loss in voltage of I * R (per Ohm's law). You can address this with thicker wires (increased cross-sectional area results in lower resistance), or by reducing the distance to the load. It is also important to note that the power lost by I * R is lost as heat, so pay attention to the thermal rating on the insulation for the wiring you use; again, refer to the appropriate safety standard.

Power converter: most commercial/consumer power supplies are rated for indoor use, where the ambient temperature and humidity are low. They may not work as intended outdoors, particularly in warmer weather; the data sheet usually specifies permissible relative humidity and de-rating values for increased temperature. The data sheet should also specify the efficiency; no converter is 100% efficient so you'll need more power in than you get out (the rest is wasted usually as heat). If the LEDs specify an inrush current--for example, if they have a lot of capacitance on the input--this also factors into the design, as you need to check that the power converter can either supply that much current, or at the very least recover from it. These factors may or may not add up to the "80%" you suggested; check the data sheets, don't guess.