Hi Intastella, and welcome to Pigeon Angels!
What a cutie you've got there!
And he looks to be a baby woodpigeon, rather than an ordinary city pigeon! I don't get those here, but they develop faster than most other types of pigeon, so your baby could be about three weeks old!
The mess at meal times is unavoidable, I'm afraid
but it may become a little less messy if you use a long, thin container, syringe or jar closed by a bit of rubber (such as part of a rubber glove), tightened and well secured with a rubber band. With a sharp knife, cut a 1 cm slit in the middle of the rubber 'lid', direct the baby's beak to the hole, hold the container almost upright (to get gravity to help you) and the baby will be able to suck the food out without spilling too much. There's really no need to squeeze the food into his beak, as squeakers suck their food.
You're quite right not to try to force open his beak to put the food inside! Many baby birds eat that way, but not baby pigeons!
What I would change is the egg yolk, which contains far too much protein for him, and may cause bad indigestion. There are recipes for baby pigeon food, but I have to say that not all babies like the taste of them... the safest bet is Kaytee Exact hand rearing formula, or a similar proprietary formula, mixed with small seeds. It contains all the nourishment and vitamin supplements for perfect growth. And adding a little live yoghurt would be great, and that's still the best kind of probiotic to give them, very important for hand reared babies to develop their immune system and resistance to disease.
It's very important that his crop empties between feeds, as any accumulation of food in the crop will rapidly turn sour and lead to a yeast infection. This is one of the most common causes of baby bird emergencies. But if he starts eating with an empty crop, you can let him eat at will -- and babies this age will eat LOTS, as they are growing so fast at that age!
He may be getting very close to being able to pick up seeds by himself. In the wild, they would copy the adults' behaviour, but you can give him a hint by scattering some seed and then forming a beak with your forefinger and thumb, and picking up seeds with them, just as a bird would peck. You would be surprised how fast they learn!
Much the same with water, especially if the first time you present it to him it is at body temperature. Put some in a cup/glass and place it under his beak, dipping about half his beak into it (no more, so it doesn't go into his nostrils). After a few tries, he'll get the idea!
Let us know how he's coming along, and thank you so much for sharing his story and pictures!