I have a pomegranate tree that I planted 4 years ago. The tree is heathy but the fruit production is not great. The flowers fall off before developing into fruit or soon after. The fruits crack open and the size of the fruit is average size but that may be a function of the tree I have planted.
In the USA pomegranates are grown in the driest parts of California ( and in Arizona ) with commercial cultivation centered in the southern San Joaquin Valley. It prefers low humidity, and long summers. The fruit takes 5-7 months to mature after blooming, and should be picked when it is a deep red hue. When mature it has a metallic ring when tapped. But if left past maturity, the fruit has a tendency to crack open, for example when rained upon.
Pruning: Plants should be cut back when they are about 2 ft. high. From this point allow 4 or 5 shoots to develop, which should be evenly distributed around the stem to keep the plant well balanced. These should start about 1 ft. from the ground, giving a short but well-defined trunk. Any shoots which appear above or below should be removed as should any suckers. Since the fruits are borne only at the tips of new growth, it is recommended that for the first 3 years the branches be judiciously shortened annually to encourage the maximum number of new shoots on all sides, prevent straggly development and achieve a strong well framed plant. After the 3rd year, only suckers and dead branches are removed.
Trees take about 3 years to start bearing fruit, but a larger crop of fruit may take from 5 years.
It doesn't look from your pictures that much, if any, pruning has been carried out. And it may be that the tree needs another year to get a good crop. The fruit splitting open likely means you've left it too long to pick.