I have an aloe vera plant and I suspect that it has root rot. If I were to cut off all the dried out leaves and replant it into a different pot, would it re-establish its root system?
It may or may not, depending on how severe the root rot is. But it's worth a try. Repotting into dry soil and letting the roots dry out is a good option. When you remove the plant from its pot, cut off any roots that have gone mushy. Also see this article on saving plants from root rot:
This is what the root of my aloe vera looks like. Is it possible for it to regrow some roots?
Yes, it might be able to grow back. Aloe vera "pups" with few roots are often able to grow on their own, so you can treat this like them. Just put it in a fresh pot of well-draining soil (preferably cactus and scculent soil), moisten it, and be sure not to overwater. It might appreciate being in the shade until it gets established again.
This past freeze I wasn't home. My aloes froze. I read to cut them back in February. Today, I did, and I hope I didn't hurt them. I have a bunch of them and a very large mama from which I got all of my pups. Did I do the right thing?
Cutting back any soft or rotting parts of the aloe is a good idea, but don't cut back any green, firm parts, since those are the parts that will grow back. I am not sure of your location, but if the chance of frost is past for the winter, and you can see some still-healthy parts of the plants, then your plants should recover. If there may be additional frosts, you'll need to protect the plants by putting cloths or buckets over them.
With a soft stemmed plant such as Aloe, you were right to prune right away.
With time, I think they will recover.
When replanting an aloe vera which has no root system, should I keep it out away from light or does it need light to develop roots?
A Aloe Vera plant needs a bright light location.
These articles will help you.
https://www.gardeningknowhow.com/houseplants/aloe-vera/aloe-vera-plant-care.htm
https://www.gardeningknowhow.com/houseplants/aloe-vera/dividing-aloe-plants.htm
The soil of my aloe vera has turned white a week after I gave it water. Will that damage my plant?
Inspect the soil to help determine if it is mold, perhaps from excess water in the soil.
Crusty white residue could be build up of salts; this could come from over fertilizing or watering with conditioned water.
Make sure the soil is well draining. Aloe soil should dry between waterings.
Try using distilled water or leave the water from you tap to set on the counter for 48 hours before using.
If it is excess salts you can try flushing the soil, but you will need to avoid overwatering.
You could also repot the plant with fresh potting mix. A Cactus soil mix is appropriate.
I'm listing a few links for you to help you.
https://www.gardeningknowhow.com/houseplants/aloe-vera/aloe-vera-plant-care.htm
https://www.gardeningknowhow.com/houseplants/hpgen/signs-of-over-fertilization-in-houseplants.htm
I have several sized Aloe Veras. I have noticed the tips on a few of them are wilting. They get light from a plant LED and the room temperature is roughly 20 degrees through winter. They are in a cactus potting soil. I water maybe once a month. What do I need to do to save them?
Though there are some varieties of Aloe Vera that can tolerate cold temperatures most will not thrive or survive in the cold.
The lowest temperatures that most Aloe Vera will tolerate is 40 degrees F.
I would move your plant to an indoor warm location.
Here are some links to refresh you n the care requirements.
Under watering will also cause the tips to turn brown and this will travel down the stem.
https://www.gardeningknowhow.com/houseplants/aloe-vera/aloe-vera-plant-care.htm
https://www.gardeningknowhow.com/houseplants/aloe-vera/growing-aloe-outdoors.htm
We have a couple of aloe vera plants that had done very well (even in cold weather the last couple of years) until we got the last frost in Houston a few weeks ago. I trim the damage leaves but the plants are not recovering and still look brownish and sick. I've transplanted a couple of the young ones but they are not picking up either. What should I do?
If the entire plant is damaged by the cold, your plant may not recover.
It does appear that some of the plant is still green.
You will need to remove the damaged and dead plant material.
https://www.gardeningknowhow.com/houseplants/aloe-vera/aloe-vera-plant-care.htm