Please see image
It is very hard to see from the image, but it appears to be a Flea Beetle! Here is an article that will help:
https://www.gardeningknowhow.com/plant-problems/pests/insects/controlling-flea-beetles.htm
Outdoor basil gets plenty of sunlight and decent watering. I've pruned and used the cuttings to root in water indoors. They've been thriving green still in water with lots of root growth. However, the outdoor basil has been looking yellow light green, but no browning or wilting. No signs of disease or pests, just common garden bugs buzzing around. I uploaded a picture of the basil outdoors. First picture is 9/18/2020. Second picture is 9/13/2020 my cutting that flowered indoor. I removed the flowers after this photo. I thought maybe it was end of cycle because of the flowers, but all my cuttings in water are thriving and fully rooted indoors with bright green leaves. Third photo is 9/23/2020 where I've kept my indoor cuttings in water. Fourth picture is 9/4/2020 when the outdoor basils were still green. Fifth picture is 9/18/2020 the indoor cuttings in water with growing root system. Still haven't attempted to try a taste of the light green leaf, but was wondering if it can revive to lively green again.
The light green is, likely, caused by nutrient deficiency. Lack of nitrogen can cause this, so it might be time to feed the plant.
Usually, once it becomes this mature, it will start to degrade in palatability. The taste will become too astringent to be of culinary value. It is best to harvest the plant and start new seeds each time around.
Here are some articles that will help:
https://www.gardeningknowhow.com/edible/herbs/basil/information-on-how-to-grow-basil-indoors.htm
https://www.gardeningknowhow.com/edible/herbs/basil/how-to-grow-basil-plants.htm
I got roughly 3 days ago watered it once and it's dead already. I never had much of Green Thumb but it's still amazing how quickly I can kill things. I think I may have over watered it but the soil was already dry due to being in a store. It looked extremely healthy when first purchased.
That does appear to be overwatering, and a lack of light.
At this point, it will be better to start over. Recovery will take a long time, and even a seed grown basil will grow faster than it will take this to recover.
These articles will help you with the care of basil in the future:
https://www.gardeningknowhow.com/edible/herbs/basil/basil-watering-tips.htm
https://www.gardeningknowhow.com/edible/herbs/basil/information-on-how-to-grow-basil-indoors.htm
This is not the edible plant. This one grows 3 feet and has beautiful purple flowers
You did not mention whether your shrub is containerized or planted outside. If it's potted, it should be moved to a garage or basement to protect it from the harsh cold of winter. If it's in the ground, you may want to mulch generously around the base, and wrap it loosely with burlap. Here's a helpful article for you:
https://www.gardeningknowhow.com/plant-problems/environmental/protecting-plants-winter.htm
This article should give you what you need to know:
https://www.gardeningknowhow.com/edible/herbs/basil/propagating-basil.htm
The basil plants I had planted in a planter outside got infected with downey mildew. I got rid of the infected plants. Can I plant new basil plants in this same soil?
It's best not to use the soil unless it is sterilized first. Here's a helpful article:
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/sterilizing-soil.htm
I grow basil on my windowsill. This morning I noticed it was covered in tiny white bugs. I immediately washed it under the tap to get rid of them. How do i stop them coming back. Obviously I eat it so what can I use that's safe?
You can use Neem Oil for pests like aphids.
https://www.gardeningknowhow.com/plant-problems/pests/insects/homemade-aphid-control.htm