Hi I can fully understand your worry. 1.As the baby grows they take more milk at one feeding session ..so they start feeding at a greater interval.. so the duration between feed increases.. 2. Babies can see everything surrounding them.. so are very intrested on what's happening around them... so its natural for them to play while feeding. See that place where u feed in quite..no disturbance of phone or TV. 3. Night time you may allow 5 hours gap.. later try to wake up amd feed.5 What is babies current weight and birth weight....  that needs to be assessed to see why he is vomiting..  you may opt for online consultation for same.

At 4 months, baby must feed every 3 hours ie around 7-8 feeds per day. Avoid bottle feeding, prefer breast milk. Awake baby once during night for feeding, 7-8 hours is a long interval for not feeding the baby. For vomitting give motinorm drops 5 drop three times a day.