First, I would recommend repotting the plant in a bigger container large enough to support it and keep it from tipping over. Also make sure it has plenty of drainage holes in the container. In the wintertime bring the plant inside and place in a bright, sunny location. When it warms up and after the last threat of frost, take the tree outside and place in a sunny location. Make sure while the tree is outside to spray regularly with neem oil as directed to help to prevent insects.
As for watering, during the growing season (March thru September) apply a soluble fertilizer twice a month. In the fall and wintertime, stop fertilizing but continue watering as before. When watering, make sure you water thouroughly and let dry out between watering. Make sure that you don't overwater.
Citrus requires minimum pruning. Remove suckers and dead or diseased wood as they appear. While you may want to shape your tree occasionally, heavy pruning may slow fruit production. If a tree becomes leggy, prune (preferably in February) to promote branching and give it more light. Trees produce heavier crops as they mature. Flower and fruit drop is common, and there's nothing you can do about it. To help fruit production, when the tree is flowering, take a paint brush and lightly move the pollen from one flower to another to help the polination process. While the tree is small, remove some of the fruit to help the fruit that is on there to become larger because less fruit can mean larger fruit.
Hope that helps.
Operational Manager at
Earl May Nursery and Garden Center in Ames, Iowa