Why not? Can you buy any other types? What is important is the supply voltage, not the type of lamps.
You may not be able to do that. The 12V system will have a larger cord and may not pass thru the exhisting conduit. Call an electricial who knows swimming pool electrical codes.
You shouldn't! That is not normal, and indicates a serious electrical problem which could very well kill you. Have it checked out by a competent electrician.
You can purchase a swimming pool light online from the Pool Supply World website. Alternatively, you can also purchase these lights from retailers such as Amazon.
Somewhere
You need the proper tools and the qualifications to do this job. Call a qualified swimming pool electrician or pool tech to do the job to code and install a GFCI. k
The lighting installed in these swimming pools are normal flouresant light bulbs within waterproof cases. The installation is actual very difficult to do. It requires draining the pool, and making indentations into the pool floor to install these lights.
because electricity spreads through water
You should never run a swimming-pool pump dry! The most likely problem, from the rather flimsy evidence in your question hinting at it not rotating, is not with the pump or its motor but a fault in the electrical supply to the pool plant, or in the timer or other pump controller.
That would depend on the type of light, the wattage, the shape of the pool and the size of the pool.
You probably need to replace the light switch
'Swimming Pool', sometimes shortened to 'Pool'.
Have a professional do it. As an insurance adjuster I had a death claim when the apartment maintenance man "fixed" the pool light and a young girl was killed by electric shock from improper wiring of the pool light.