I’ve gotten a baby cocktail 2 days ago. He seems to be warming up to his cage now and not as clingy to me and started eating yesterday when he was on me. But I haven’t seen him have any water. Should I be concerned?
He's begging you to feed him. You can hold some food in your hand for him to eat (something that he's already familiar with). This is very common with recently weaned babies who go to a new home. They know how to feed themselves, but they're looking for reassurance that somebody is there to take care of them.
If you offer him a shallow bowl of water that's big enough for him to wade in, he may get in and splash around and drink some water while he's at it. Otherwise you can try offering him some kind of wet food (like seeds that have been soaked in water, or some oatmeal on a spoon), and try to get some moisture into him that way. Hanging up some leafy greens for him to chew on is another way to provide moisture, but if he's not familiar with them then he might not go for it.