I'm not an expert but I'll give you my opinion on this. It may not be right and exactly what the others say, but here's my view.
It's normal for birds to only eat seed as it is commonly the first thing they eat from when they were babies and even in the wild as it is in high in fat and I guess, more tasty and appealing to them then healthy and beneficial pellets (it's like you preferring chocolate over vegetables). Plus, they aren't used to eating pellets and they don't knw what it is. It's better for you to start converting him to pellets now than later as it will be harder to convert him later. Of course, don't just suddenly throw out the seed bowl and then replace it completely with pellets, start slow and with a few pieces. When I did it with my birds, since the pellets I ordered online were way too big for them and a bit hard to chew, I'd crush it into bite sized pieces that makes it more easier for them to eat. For the first few days, with the crushed and tiny pieces of pellets, I would hand feed it to them and not place it in their bowl. I wanted to get them used to the look, smell and taste of it and to not be afraid. I would place bits of pellets on my hand with some millet and seeds so they could get used to it and at least get a taste of it all. Gradually, i increased the amount of pellets and decreased the amounts of seeds and millet (while still, hand feeding it to them). Once they weren't too afraid of the pellets and not just throwing it out but actually eating it, I then went back to square 1 and placed a few pieces of pellets in their food bowls. By feeding them the pellets by hand, I now transferred it to the food bowl and that way, they are less afraid and are more keen to eat it. Gradually and slowly, I increase the amount of pellets given. I gave them I think about 4 tablespoons of seeds and a quarter of pellets. Overtime, it went from that to 3 and a half tablespoons of seeds and a quarter of pellets, then 3 tablespoons of seeds and a half a tablespoon of pellets etc etc. Now, I feed them about one and a half tablespoons of seeds and one tablespoon to one and a half of pellets. You don't have to do it like this exact measurement, but the idea of gradually increasing and decreasing will help.
Again, you just have to take it slow and you don't want to freak your bird out and suddenly make them think why suddenly the food has changed.
To help him eat more fruits and vegetables, I would make it into small pieces first, sprinkle a bit of millet and seed on top and let them devour it. At first it'll be a trial and error. Whether they will like it or not. But you have to keep trying. At first, my birds didn't want to eat brocolli and apple and carrot. But after the second, third and fourth try, they had a go at it and now loves it.
Once you notice them eating it, you decrease the amount of seed and millet gradually until you're left with just the fruit/vegetable. When they're used to it, they'll happily eat it off your hand. Sometimes, when I feed them new fruits/vegetable into small pieces, they take a little nibble at it first and then after tasting it, they devour it in one go!
Some healthy options you could feed him could be pear, carrot, kale, brocolli, apple, banana, watermelon, corn and hard boiled egg and egg shells (which all of these, I feed to my birds).
About only feeding him twice a day, although the website says it's an idea that is safe to do, I personally wouldn't want to do that with my birds just because what if their appetite changes, or when they suddenly get really hungry (eats more possibly in moult or breeding conditions) and/or if for somehow, you forget to put the food bowl in the cage). There may be others on this page that would/does this method but I'm a person that would just give them their regular food and leave it in their cage and not touch it unless it's empty, full of hulls and/or dirty.
I'd rather just leave his food in the cage, and if you really are concerned of him getting fat or whatsoever, just give him a good diet with a variety of fruits/vegetables and exercise.
You are doing great with the bonding. Just be patient a bit more, it'll pay off in the end!
Great job in the taming process!
Putting on some soft/gentle music, the radio/tv, your voice, reading a book and your presence will boost your bird's confidence and it'll make your little bird feel more comfortable. Don't try to overthink too much of stressing it out because it may in the end, stress him out even more. Just remember to walk gently around him, no surprises or sudden loud noises, don't grab or chase after him, put him in an area where it's not too lonely yet too noisy and just be there with him. Remember to first put your hand in the cage not too close to the bird but at the bottom of the cage for a few minutes a day, talking to him and gradually and slowly put it closer to him. He'll eventually realise you're not a threat.
Good luck and I hope I helped!
May I ask what the name of your bird is?