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The location near an air conditioning unit is likely some cause of your issues.
I would move to a location that would meet the ferns needs.
Here are links for you with more information.

https://www.gardeningknowhow.com/houseplants/boston-fern/boston-fern-care.htm

https://www.gardeningknowhow.com/houseplants/boston-fern/boston-fern-misting-needs.htm

https://www.gardeningknowhow.com/houseplants/boston-fern/watering-boston-ferns.htm

I would use Neem Oi instead.
This is safe for people, pets and bees.

It works as both an insecticide and fungicide.
You can use weekly until the issue is resolved and even preventatively.

Here is a link for you.

https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

If the fern were outside in nature, those runners would root where they touch the ground, giving the plant another means to spread. You can cut them off.
https://www.gardeningknowhow.com/houseplants/boston-fern/boston-fern-runners.htm
https://www.gardeningknowhow.com/houseplants/boston-fern/boston-fern-care.htm

Yes, bring them indoors prior to the first frost. If you reduce the light and cut back watering, the plants will go dormant. You can put them into dormancy at 50-55 F. Find a cool, dark place (a closet or a basement) and put them there. Storing in the garage will be fine provided it does not get too cold (below 45-50 F). Cut back watering to about once every 3-4 weeks. They will look like they have died but they will come back. In the spring, bring the ferns back out and resume normal care.

It could be stressed from repotting and be overwatered.

Here is a a link to refresh you on the care.

https://www.gardeningknowhow.com/houseplants/boston-fern/boston-fern-care.htm

It may be trying to go dormant, or it could be pot bound. You can cut the plant back, or in hte very least, cut back the yellow/brown foliage. Here is more information: https://www.gardeningknowhow.com/houseplants/boston-fern/trimming-boston-ferns.htm