Some trees may develop branches that go in odd directions. These can be pruned anytime. The trees will develop a nice round shape naturally, without much pruning. To speed this up a bit you can pinch off the tips of new growth. Flowering is not a seasonal activity for citrus.
Citrus can flower at any time as long as temperatures are warm and rainfall is regular.
Often both flowers and fruit can be found on the tree. I recommend bringing the tree indoors to a very warm area with at least 60-70 percent humidity to cause it to flower. Acclimatize the tree by setting it in an intermediate area for a few days, so it can adjust to the new digs gradually, or it may experience leaf burn. When growing your tree inside, after flowering, you will need to use a small paintbrush or cotton swab to transfer pollen from one blossom to another to insure fruit set. Sometimes a light shaking of the tree will transfer pollen as well.