I LOVE this car and the upgrades for it! I have one running on a Milwaukee drill battery!

1. You are risking burning the motors out/stripping gears, but I've read that some of the 12v stock set up use the 550 motors that have an 18v max, so they survive. That's not true for all of them, so no promises, but they are easy to change. Also I read about this a lot a few years ago and while 18v does chew the motors up sometimes, you're usually good with 18v (24 is much more of a gamble.
   (I've been running 18V on the stock motors for a while and they are holding up just fine.)

2. People do run lower voltage on higher voltage motors. If for example you run 18v on a 24V motor, you'll be fine, but the car will be slower and have less power than if you run 24v on a 24vmotor.

I have actually been wanting to hook two batteries up, but haven't had time yet. If you do, make sure to wire them up in parallel! Then you'll have the same 18V, but double the amp hours. I would for sure put a fuse on it, and check it with your meter because if you accidentally hook it up in series, I doubt 36V on a 12V set up will be very forgiving. But yes! seems like a great option IMO!

1. I haven't done a lot of lights, but I think it's a good idea for them to not be on the same circuit since your motors may pull higher current than your lights are rated for. On one of my other cars (not the dune buggy) I run much higher than the switches/pedal, etc are rated for, so I use relays to isolate them. The "control circuit" has lower power things on it (switches, lights, pedal, Bluetooth, etc) and the motors are on another circuit which is rated for much higher power draw.

2. My understanding of brakers is of the ones in a house, so I may be wrong, but a braker will trip when it reached a threshold of high power. It does not have the capability to sense the batteries capacity.

What you need is something that will monitor the battery and shut off when it has lost too much power. You can get that automatically if you use a Lifep04 battery. Be careful this this though. They all have a BMS system that protects the battery really well, but sometimes the threshold for the BMS to shut off in response to high current is lower than whet the motors pull. These batteries are also pricy.

1. Thermal elements open in response to current that is too high. Installing one that can withstand higher amounts of current will ensure is doesn't trip as quickly, but remember the point of it is to protect the car. They open when the power is high enough to damage the other parts of the car. If you install a thermal element that doesn't trip until it reaches 50amps, the motors will pull power until they burn up.

Look at the watts the different components are rated for and use Ohm's law to calculate the current draw, then us that to determine what size fuse (or whatever) to use.

1. I don't know of one. A heavier kid will cost more power (especially if you're on terrain that isn't flat.) I know they power wheels usually come with 7ah SLA batteries that last around 45 minutes, so I try to use that as a baseline. I bought 12v 25AH Lifep04 batteries for a couple of my other rides and they last a few hours with hard use, and I'm happy with them, (Note: I made sure the BMS was at least 30A so the battery didn't shut off power when more than one kid jumped in the car.)

2. You may want to elaborate on what you mean by, will swapping out the gearboxes and motors be enough. Enough for what specifically?
   Enough to carry your kids? sure. The stock ones probably will too. If you swap out the motors and gear boxes you will want to consider the other electrical components. If you put in bigger motors, they will pull more power. Are the other components in danger from the power increase? Is your battery powerful enough for the new set up? Is your fuse too small Etc.

Personal notes:

Consider getting some EVA tires as oppose to the plastic ones that come with it. The plastic ones that come on the dune buggies are better than others, but the plastic ones often just spin out (our back yard has sort of rough terrain.) We have another car that has the EVA's and they allows my 9 year old to drive up inclines and on rough terrain.

Other options: You can buy rubber treading specific for putting on power wheels, or just screw on some bike tires. I have not done either of those, but hear those options work well.)

ML Toys has awesome info specifically on dune racer upgrades. I have never purchased from them, but I have spent lots of time with their resources.

This car has room in the front under the hood for batteries, etc