The answers to most of your questions depend on where in the world you (and the tree) are living. Adding your location to your profile helps us help you.
Your bonsai is a Ficus. They are called Ginseng Ficus because of the exposed roots (like a ginseng root). Yours has been grafted with a small leaf, compact growing, variety of Ficus. If you see shoots that grow faster, longer or have larger leaves you should chop them off. If left to grow those will overpower the neat grafted section.
Ficus cope with repotting better when they are actively growing so would be best in late Spring or Summer - depends where you and the tree are living.
Water only when the soil gets close to dry. Don't be fooled by surface dry. Need to drill down a bit with a finger to check below surface soil moisture. How often depends on many factors - time of year, location, aircon, drafts, sun, temperature, etc so there's no way of advising to water every x days and that will change through the year anyway. keep checking soil before watering. One good thing about ficus is that most types are very tolerant of dry so the soil can get quite dry without immediate harm. My guess is the outer pot has no drain holes. Constant wet roots can cause problems long term so make sure the pot is not sitting in water. Best to take it out of that outer pot, water over the sink, allow to drain before returning it to its home so you don't have the roots sitting in a pool of water.
Any plant fertiliser is good for bonsai and for Ficus. Find something that's convenient for you and easy to use. We tend to fertilise more often than most plants because we also water more often. Watering leaches nutrients out of the pot so we need to keep adding more to replace. It's not unusual to fertilise every 2 weeks when the tree is in growing phase (which will depend on location and local conditions)
Ficus are one of the few trees that can survive indoors without direct sun. They certainly do better with good light, some sunlight or a grow light to give enough light energy for healthy growth. Good light is important but, too much afternoon sun through a window can be detrimental. We'd need to discuss your specific room conditions to be able to advise for optimum placement.
Initially, pruning is only needed to manage long shoots. As the tree develops you may want to change the trunk and branch structure to look more like a real tree rather than a ball of leaves on a stick but that's well in the future. Spend the first year learning to keep it alive and healthy. We can go further when you have that part mastered.