I haven't raised a calf but I highly recommend you find the relevant info rather than wing it. You sound like you're doing ok, but I'd back off the eggs a bit, and definitely find the right info ---- maybe the dairy you got him from will help? Generally the milk replacer bags will have the info on them for dosage.
Overfeeding is at least as deadly as underfeeding, often more so, and incorrect feeding is also just as bad. If you don't know what to feed him you're likely to give him pulpy kidney or some other ailment which you can lose him to. As far as I know, the raw eggs are fed as an alternative to colostrum; he might have gotten some colostrum but continued consumption of raw eggs will be an issue for many ruminants. Some others don't seem to have an issue with it though. But it is animal protein and he is a herbivore; at this point in his life the only raw animal protein he should be having is unhomogenized and unpasteurized milk, or a milk replacer with probiotics in it. I'd think you can raise him on raw goat's milk but best to check up on that.
What sort of milk replacer are you feeding him?
Also, I'm not sure he'll make a good ox. When you say 'ox' I think 'bullock' or draught animal, used to work; maybe you just mean a steer? As in, desexed to fatten to be eaten? Sorry, I don't understand exactly what you mean there.
A Jersey though isn't going to make a great worker if that's what you've planned for him. But that's not to say he won't be any use whatsoever.
I am not a fan of desexing unless for medical reasons, so personally I wouldn't desex him if he were mine. Good bulls remain good despite having testicles, and bad bulls remain bad whether or not you remove the testicles. His temperament depends a lot on how he's raised, but also on his parentage. While his mother probably contributed some trusting mentality patterns to him, there's every chance his father didn't, since the breeders of Jerseys have been remarkably slack when it comes to making sure good genetics are only bred when matched with good temperament. Many other livestock breeders make sure of this combo in all breeders, male or female, but commercial Jersey breeders have been a bit too focused on yield, in my opinion. Some of them keep 'battery bulls' which have a life rather like a battery hen, which is not conducive to sanity and sociability.
While he might remain calmer if you desex him, he won't grow properly; the sex hormones also have influences on the bone structure and general vitality, so I'd wait until he's older if you're planning on using him as a worker. If he's just a pet it shouldn't matter too much.
But from what little I know of banding, it's much better done sooner than later; in fact I think there's some sort of law against doing it later in life due to the sheer amount of pain it causes. I was present when a ram lamb was banded at a few months old and he was definitely in agony. He threw himself around and smashed into things and rolled madly. Not advisable. If you wait until he's older to get better growth on him, then a different and more expensive castration method would need to be used --- I think; I don't know how it goes where you are.
Anyway, best wishes.