Congrats on your new banana! Bananas grow best outside during the summer months, esp when the heat and humidity are the highest. Since you stated that you live in an apartment, planting outside or putting the pot outside is probably not an option.

For the pot size and rooting, I would tend to favor a wider pot, but less depth. The reason is during the winter months, bananas are very susceptible to root rot. The deeper the pot, the more water remains in the bottom. Bananas use much less water in the winter months. I would replant your banana in a bigger pot, but consider more width and less depth. Cavendish bananas are more prone to rotting than most other varieties.

Any kind of potting soil is good. I myself use Miracle Grow. Generally, you want a well draining soil.

Misting is good, but humidity is better. Misting is preferred in the winter months, during times of low humidity. Air conditioning will obviously lowers the room temperature and with that, you get drier air. I myself do not like air conditioning, except for the computer room that I have all my computer stuff in. Since you have the pot in the apt all the time, try to leave some windows open for humidity in the summer and mist as much as you can in the winter months.

Yes, bananas are prone to spider mites. I've only owned a few varieties of bananas. Super Dwarf Cavendish, Ice Cream, Dwarf Orinoco and Basjoo bananas. Out of all of these, to me my Super Dwarf Cavendish ( SDC ) have had problems with spider mites. Why, I don't know. For spider mites, a solution of warm water with some dish detergent mixed in helps if you SPRAY this solution on the plant.

In the winter, do not fertilize. Water very lightly. Wait till the top inch and a half is dry. Like I said above, the Cavendish varieties of bananas are very prone to excess watering and can cause rot.

Since your banana is in a pot, cut off the leaves and discard when they are fully brown. It will help your plant look neater and dead leaves in the pot will contribute to pests. The leaf, when dead cannot process any sunlight needed for photosynthesis.

As far as which window, pick one which receives the MOST sunlight. Any kind of banana will fruit, provided the main stem ( psuedostem )does not die. There are a certain amount of leaves that are needed to grow before the plant flowers. In your case, you may need anywhere from 32-40 leaves during the growth process before flowering occurs. You may notice that your banana will produce small offsprings which we call here, pups. Try to keep the pups to a minimum of 3. I would wait till summer when the banana is actively growing to separate the pups from the mother plant. This involves cutting the pup down to the root level and cutting off a piece of the corm with it. The newly cut pup may be repotted in another potor discarded. You could always give away the new bananas to whomever wants a banana. I only say this because keeping the number of pups to a minimum will help the banana to flower. There is no harm in letting all the pups grow. The corm is the main part of the banana which is located in the soil. It looks like a tulip bulb, but it isn't a bulb. From the corm grow the roots downward and the stem upward. Did you know that the banana is actually a herb. The stem is not a real trunk, unlike a tree since it has no bark. The stem is actually all of the leaves that compose of the stem and will eventually grow out to produce leaves.