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Oh my!
You may want to try placing section into smaller pots.
These links will help you.

https://www.gardeningknowhow.com/ornamental/cacti-succulents/string-of-pearls/string-of-pearls-plant.htm
http://www.desertplantsofavalon.com/how-to-propagate-the-string-of-pearls-plant-senecio-rowleyanus/

Once a week may be too often. It is best to check the soil instead of watering on a schedule.

This article will refresh you on the care requirements.
https://www.gardeningknowhow.com/ornamental/cacti-succulents/string-of-pearls/string-of-pearls-plant.htm

Yes. You are correct in your assumption. These require bright sunlight. They can be grown, happily, in full sun.

Here is an article for further care:https://www.gardeningknowhow.com/ornamental/cacti-succulents/string-of-pearls/string-of-pearls-plant.htm

Yes, they will do well under horticultural lighting. The succulent mix, whether sandy or not, will be most suitable for these plants. Just don't let them dry out too much, as they like lightly moist soil.

I recommend only watering these plants every 2 to 3 weeks. they are very drought tolerant. Also, they tend to like high amounts of light, so make sure they get plenty. Here is an article that will help: https://www.gardeningknowhow.com/ornamental/cacti-succulents/string-of-pearls/string-of-pearls-plant.htm

Although these plants resemble succulents, they are actually better suited for outdoor growth. They can do well indoors, though with little care. They need as bright of light as you can possibly give them, and require a somewhat moist soil with dry periods in between. They are pretty drought tolerant though. If you are afraid that you have overwatered, then put a bright CFL or LED bulb over them until they dry out some. Even then you may want to keep this on the plant if it does not receive bright light for most of the day.

This article will give you more information on this plant: https://www.gardeningknowhow.com/ornamental/cacti-succulents/string-of-pearls/string-of-pearls-plant.htm