Which country are you in? Sorry I was assuming you were in the Uk. In terms of diet they just need one good hamster muesli mix that contains the right levels of protein and fats. You can usually get Tiny friends Harry Hamster in most countries and that is fine for a dwarf hamster as well. It contains everything needed and whole sunflower seeds and peanuts. I wouldn’t give vitakraft drops. They don’t need added vitamins if they are on a good mix with the right contents (Harry Hamster also contains all vitamins and minerals needed). They can actually have too many vitamins. If he was ever sick or needed extra vitamins the best way to achieve that is to give a pinch of hemp seeds daily - they also contain all vitamins and minerals.
No they don’t need hay. That’s more rabbits and Guinea pigs. All they need is plenty of substrate (paper based better than wood shavings. If you do use wood shavings they need to be kiln dried pine and dust extracted (never cedar or unspecified wood). If it doesn’t say kiln dried pine on the pack it’s not safe.
So plenty of substrate - at least 4” deep. And plenty of toilet paper strips for nesting - and that’s all you need - apart from a house, wheel, some tunnels and other toys/hideouts and a shelf ideally. Plus food and water.
If you do get Harry hanster then freeze that too! Never had an issue with that but after an outbreak of moths from food (which infested my home!) I now freeze all hamster food for a week.
Won’t suggest any more pet disinfectant till know which country you’re in! Amazon sell it too but it’s more expensive there. In the Uk most pet shops stock it.
The taming sounds to be coming on really well - pleased for you
. Don’t worry if you have a set back after the cage clean - he just needs some time.