Am I doing it right? Is self-feeding a good/viable option?
Not every cat is equally adept at self-regulating their food; but I expect a vast majority of cats to be able to learn this skill if they do not already have it.
Because he's a rescue, he's more likely to eat all that he can, because a cat in the wild is never sure when the next meal is going to arrive. It might take him longer to learn how to self-regulate, but he should still be able to learn it.
For the last month approximately, he have been trying to teach him to self feed, giving him all his 3 meals together in the morning (7am, maybe 9-10 the weekends), but he always eats everything before 12am.
Your cat has likely become reliant on your suggested meal sizes. If the three meals you've been giving him have been on the small side for him (where he always wants to eat the whole thing), then your cat likely has unlearned to gauge how much they should eat in single sitting.
Your cat is very likely to overeat if you suddenly start giving him a large bowl. Just like how a child who is given free access to the candy cupboard will eat candy at a record rate (until they feel sick, at which point they learn to not gorge themselves). Just like that child, your cat will need to learn a new skill: keeping leftovers so that he can eat them later.
It's normal for him to struggle with it at first. Every creature needs to make some mistakes, so that they can then learn from their mistakes.
Then for the rest of the day, he keeps asking for more, yet again, can't tell if he is hungry or just likes food.
The fact he asks for food proves to you that he hasn't learned to self-regulate. He should've been smarter and left some food in his bowl so that he can eat it now.
Do not feed him. The inconvenience of feeling hungry is supposed to be the incentive for him to learn self-regulation. If he self-regulates, then he won't feel hungry.
If you feed him, you preclude him from having to learn from his mistakes.
If it's been a few days, and he still hasn't learned, maybe you should intervene. The problem with consistently overeating is that it stretches your stomach. If your stomach stretches, then you need more food in order to feel full. Consistently overeating can lead to your cat being able to easily eat the whole meal in a single go, which makes it harder for him to learn how to keep leftovers.
However, if you go back to the old feeding schedule, you're again putting him in a situation where he doesn't need to learn self-regulation, which is also not good.
If you suspect his stomach has already stretched, it might be beneficial to go back on the three-meal-plan for a short while, so his stomach can get used to eating smaller portions again.
Solution 1 - Free, but requires training
Serve him all the food, but use two bowls, and cover one bowl so that he cannot eat it. Ideally, a transparent cover, so that your cat sees the food and knows that it is there.
You could also use clear plastic containers with lids, in case your cat is clever enough to lift a cover.
If he asks for food later in the day, simply remove the cover from the bowl, giving him access to it.
It subtly suggests to the cat that the food was there all along, which should eventually make them realize that they have the ability to leave food for their future (hungry) selves. How quickly he learns this depends on the cat.
Solution 2 - Costs $20 but works well
We bought our cats a food maze:
The idea is that you put food in the top, and your cat needs to push the food through little holes, so that it drops down and will eventually land in the dish on the ground.
The idea here is that it costs effort. When he's hungry, your cat will be more than happy to spend that effort to get food. However, when he's not that hungry anymore, the food will no longer be worth the effort, and he'll stop eating it.
I was apprehensive of this; I figured that any cat who is determined to finish their bowl will be equally determined to empty the cat maze. But I have to say that I was proven wrong, because it did wonders for our cats. The friends who suggested the maze to me have had equally good results with their cat (who is left by himself for a day more often, and thus needed to self-regulate).
There have been days where I've poured in too much food by accident, and I've noticed that a larger pile lasts for longer, so they're not eating more than usual just because they have access to it.
One thing that I realized at a later stage is that when you put enough food in the maze, then the initial food is easy to get (a simple swipe will make many pieces drop), but it takes more and more effort to get food when the maze is nearly empty (because you need a precision swipe just to get a few solitary pieces).
This again incentivizes the cat to stop eating afte a while, and come back when he's sufficiently hungry (and therefore sufficiently willing to put in the effort).