Ow that is a young pigeon. He either just left the nest or needed just a few days to leave it.
He is able to eat on his own but probably would need some encouragement. You can put seeds in shallow bowl in front of him and just tap with your finger imitating like you are pecking the seeds. he will get interested and watch. Same for water.
You can give some defrosted peas via beak - take frosted peas, put them 30 min in hot water - hot from the tap, not boiling! After 30 min you get rid of the old water that will now be cold and put in some warm water again, just warm to the touch and leave for a minute or two. Than wrap him in towel so that only the head sticks out, take some peas and give directly in the beak. Don't give much, maybe 5-6 for the begging. Then let him out of the towel, take a cup full of water and bring the cup to his beak so that 1/3 of the beak gets in the water, he should drink on his own. After he drinks he will start to shake his head which is a sign he doesn't want any more water. Keep him calm and warm.
Vet should look at the leg, looks broken but probably much higher than a foot, probably broken femur. Birdie will probably need some antibiotics, maybe something to manage swelling so that nerves are not damaged.
Baby should eat on its own and drink on its own but you should monitor via poops. His poops on the photo look good, but if the colored part becomes very small, or like a small slime ball he is not eating.
And of course please remove the granules for the gerbil, they are not got for him and can cause problem.
PS it is probably 25 day old feral pigeon, it is a bit confusing as he is black with pale eyes, not a usual color for pigeons. The chirps you are hearing is squeaks that young pigeons make, you can type in "baby pigeons squeaking" on you tube and hear the sound.