It is probably either a Ginseng or a Retusa. However, in terms of care, it really makes no difference. It will probably lose some leaves if the light is changed significantly. Bonsais do best indoors year-round in a sunny location. There is no advantage to moving it outside in the warmer months, but if you do, keep it in light shade.
The whole point of Bonsai is to keep the tree miniaturized. The only way to do that is to prune back stems and branches regularly so it never gets much bigger than it is now and so that it maintains its overall shape. It will also never need a larger pot. Because it is in a small pot, it is very hard to overwater unless the pot has no drain holes.