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They are normally well suited to growing against a warm wall on the south side of the house. This article will help with the moss: https://www.gardeningknowhow.com/ornamental/foliage/moss/moss-on-plants.htm

You could but it would really have to be diluted in order not to hurt your hibiscus. Then it would likely not affect the spider mites though. I would instead recommend using neem oil to treat the spider mites. It is very effective on these pests and will not pose any harm to the plant or you. Here is more information: https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

The following article should be of some help to you: https://www.gardeningknowhow.com/ornamental/flowers/hibiscus/answers-to-what-causes-hibiscus-leaves-turning-yellow.htm

Yes, it will do fine in morning sun. Just keep the plant protected (move to shady area or provide shade cover) from the most intense sunlight during the hottest part of the day if possible and provide plenty of water.

Yes the blooms only last a day. While you can deadhead if desired, this practice is not necessary. Your hibiscus plant will be fine left as is. The spent blooms will drop on their own. Here is an article that you may find helpful: https://www.gardeningknowhow.com/ornamental/flowers/fgen/deadheading-flowers.htm

The proper time to transplant the hibiscus is anywhere in late fall or early spring, depending on how cold your climate is and the variety you're growing. Hibiscus enjoy warm, sunny conditions, especially the tropical variety (which should remain in these conditions). However, hardier varieties can withstand cooler temps.