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It sounds like you have a pest of some kind, either aphids or spider mites, most likely. These articles will help:
https://www.gardeningknowhow.com/plant-problems/pests/insects/spider-mite-treatment.htm
https://www.gardeningknowhow.com/plant-problems/pests/homemade-aphid-control-a-natural-way-to-kill-aphids.htm

Do not worry too much. Most likely this is from its adjstment to the indoors, which typically contains drier air than outside. It usually helps to mist plants or add a humidifier to increase the humidity level in the home. You might also want to trim out the brown foliage. Another cause to browning comes from the type of water you give it. If it's acustomed to receiving rainwater, then regular tap water (which is usually full of chemicals) can cause the plant to brown. Try some distilled water or leave the tap water sitting out awhile before use if this is a problem. Here is an article that you may find helpful: https://www.gardeningknowhow.com/houseplants/spider-plant/pruning-spider-plants.htm

You should cut them near the spiderettes. Some spider plants can grow several spiderettes on the same shoot, so leaving the shoot intact as much as you can may allow additional spiderettes to form.

For the brown tips, you can simply cut off the brown portion or the entire leaf. Either way is fine. This article should also help: https://www.gardeningknowhow.com/houseplants/spider-plant/pruning-spider-plants.htm

It sounds like it could be scale. I would treat the plant with neem oil. This article will help you with that: https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

For more info on scale, this article will help: https://www.gardeningknowhow.com/plant-problems/pests/scale-bug-how-to-control-plant-scale.htm

It sounds like you may have just a very healthy spider plant. Strong leaves will grow up instead of outward, though eventually they should grow tall enough that they fall outward.

Spider plants actually do better being crowded together. They produce more spiderettes when they are crowded. They also do not need much fertilizer, though the soil you are using sounds like it may have fertilizer in it, as they are growing well.

Just to be sure, make sure the plant you have is actually a spider plant. There are a few houseplants that look similar except for their growth patterns (i.e growing up instead of growing out and down).