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The issue is probably more about how much sunlight the plant is getting. It can be very difficult in the winter to get a hibiscus enough sunlight to both grow and flower, particularly if you have brought it indoors. Winter sunlight is just not as strong as summer sunlight. I would recommend trying a plant light on it. That may help, but you still may have to wait for spring for the best blooms to return.

I would wait until spring to fertilize. No matter what you do in the winter, your hibiscus is going to look a bit ragged. They are not an indoor plant and being indoors is just good enough to get them to survive. If you give them fertilizer in the winter, it could be too much and could hurt them.

It sounds like sooty mold. This article will help:
https://www.gardeningknowhow.com/plant-problems/disease/how-to-get-rid-of-sooty-mold.htm

It is hard to say for certain as applies to pigs, but hibiscus is not toxic to humans. Pigs are very close to humans from a biological standpoint (even at one time being used for heart transplants) so we suspect that the hibiscus would not be toxic to pigs either. But, just in case, keep an eye on him and try to keep him away from the plant.

Yes, you can do this. Make sure the location is cool (not cold) and that you dip the roots in water once every 4-5 weeks while you are storing it. It will look dead during this time, but in the spring, when it is planted again,it should come back fine.

Cover the plant with a sheet or blanket. Make sure to remove it first thing in the morning. This will help insulate it from the cold.