Hi.
Case 1
It is a pyloric stenosis.
I am based on the fact that in this pathology, there is a thickening of the pylorus muscles and they acquire an abnormal size and prevent the passage of food to the small intestine and therefore the children vomit in projectile, they are hungry, dehydrated and do not gain weight. The diagnosis is made through a barium x-ray and an ultrasound
The resolution is surgical.

Case 2
In a baby with hypoglycemia and palpable liver, you should think about a glycogenesis. This is a hereditary disease and there is accumulation of glycogen in the liver and kidney and this explains the low levels of glycemia and high levels of uric acid. How is not my area I would send it to the child endocrinologist.
Caso 3
In this patient I would think of an ectopic thyroid, because it has no troublesome symptoms in the oropharynx and the base of the tongue is the most common situation of thyroid ectopia.
I would perform a thyroid gammagram and would have to keep it in control simply with thyroid tests.