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It could possibly be baby ferns. Boston ferns do develop ball looking growths on the end of root like structures, a little like spider plants do. These balls can develop into new ferns, but if the plant is periodically stressed from something, like a lack of water, it may be discarding the immature ferns.

First of all, you want the plant and the soil level to be at least 1" below the rim of the pot, so you can water without having the water run off the plant and onto the floor. If you're sure you need to use this pot, you can - take a big breath now, this is scary stuff - cut the bottom off the fern's root mass so it will fit down into the pot. Just pull it out of the pot, lay it down on a cutting board, and cut off the bottom inch or 2 inches or whatever you need with a sharp knife. Make sure you allow for some soil in the bottom of the pot before the plant goes in.

You can cut the plant back, or in the very least, cut back the brown foliage. Here is more information: https://www.gardeningknowhow.com/houseplants/boston-fern/trimming-boston-ferns.htm

Yes, this will work fine. Water only once a month, but water thoroughly when you do. They will look dead, but in the spring, take them back out and the ferns should regrow fine. Here is pruning information: https://www.gardeningknowhow.com/houseplants/boston-fern/trimming-boston-ferns.htm

While Boston ferns typically prefer to be kept a little pot bound, if it is getting difficult to water, especially if the water doesn't seem to be penetrating the soil well, or if you see roots coming from the pot, then it is probably a good time for repotting. In this case, you would go up a couple inches in diameter or two pot sizes. You can also remove any old or dead growth during this time.

Here is an article that you may find helpful: https://www.gardeningknowhow.com/houseplants/hpgen/learn-more-about-repotting-houseplants.htm

Boston ferns will not usually handle cold winter weather or freeze damage well. However, you can put them into dormancy by placing them in a sheltered area (a cool, dark place) like an attached garage or a closet. Water only once a month, but water it thoroughly when you do. It will look dead, but in the spring, take it back out and it should regrow fine.