Leolady

H have a small naner that I have grown from a small corn I was given, First it had spider mites that I didn't see until the 2 leaves that had grown had both turned brown. My sight isn't what it should be, and I am having cataract surgery Tuesday. Anyway, I cut the leaves off, and sprayed the stem and soil with a mix of liquid dish soal and water. Each day since, the stem as been getting brown from the top down, and now I have maybe 2 1/2 inches of mostly green stem left. There is a brownish/black spot about the size of a dime about 1/2 inch above the soil, but it is solid so far. This has all been within the last week. Also it has stayed very moist. No drying at all. So I took it out of the pot to let it dry some. It is very well rooted.

My questions are as follows.
Do you think this can be saved?
Do spider mites stay in the soil?
Would putting the pot of soil outside to freeze get rid of the spider mites if they are in the soil?
Do spider mites get/stay on the corm and roots?
What should I do with the naner plant/stem and roots?
Will the dish soap harm the plant/roots?

I am really new to banana plants and haven't a clue what to do. I would really hate to lose this plant.

I do have 2 other naners that I just purchased. A super mini dwarf cavendish and a basjoo. They are isolated in another room and I am misting them twice a day.

Any help would be very much appreciated.

Bonnie.