As long as it gets lots of sun it should do fine indoors. Cut waaaayyyyy back on the watering though. I live in sunset zone 13 (very arid, AZ desert, in a valley) and if I water my outdoor aloe vera once a month, that is too much, especially in the winter. It rained 3 times last month and my aloe is currently limp and slightly yellow/brown from having wet feet. It will recover once it has dried out.
If the mold/fungus persists, try giving it a light milk/water solution once the soil has dried out. Should knock out the fungus. My second thought on the fungus is, it's probably in soil that is too rich and has organic matter mixed in. You want the most nutrient deficient, alkaline clay soil you can find. No organic matter or fertilizer should be added, and the soil needs to be well draining. Your native soil is probably too rich for it too, so, you may not want to plant in the ground, if at all possible.
This plant will grow progressively larger every year, and like valley said, can get as large as a house. They are native to my region and produce pups even in a cramped pot. I use it extensively for sunburns and still have to cut out huge sections to keep it manageable. If I put it in the ground it'll spread like crazy, both from seed after it flowers in the summer and budding off pups. If you do plant it in the ground, put a border around it, just in case. I don't know if it is hot/dry enough for an aloe to bloom in the south.