Your baby could be about 6 weeks old. It is hard to remember what they look like at that age.
When you feed you need to make sure the temperature of the food is between 105 and 108 degrees fahrenheit. If it is hotter then you can burn the crop.
You are doing right by feeding 4 times a day right now (in the morning (7 or 8am), lunchtime (12 pm), dinnertime (5 pm) and right before you go to bed (10 pm). When he starts to refuse eating at a feeding on a frequent basis is when you reduce a feeding. When you get down to 3 feeding go ahead and have some food in the cage for them to pick at like pellets, seed and millet. I would wait to introduce veggies until he is down to 2 feedings a day.
For heat - try a heating pad under one half of the container to keep warm - being as he does not have many feathers right now - you may also want to cover the top some to help keep the heat in the container. If he is too cold then you may run into some problems with digestion.
IRNs do not take a lot of formula so 10 ccs is about right. If you are using a bent spoon then keep doing that (using a spoon - you do feed from the front). It is the best way to feed if you have never fed a bird before as it will be harder for you to aspirate it. When the crop is full it should feel kind of like a water balloon that is not real tight. And yes, you need to make sure the crop empties at least once during a 24 hour period, like overnight, otherwise you may have things like crop stasis etc to deal with. The food consistency sounds about right - just make sure it is not too thick. I have always compared it to the consistency of pancake batter. He will get his fluids from the formula you feed him - no need to give water by itself at this time.
I would also make sure to keep an eye on his weight. Use a gram scale to keep records of his weight so you can make sure he is not losing weight and is gaining on a steady basis.
If at all possible, I would try to keep in contact with the person you got the bird from for any advice you may need as well. It is sometimes easier if there is someone in person to help with questions and concerns.