Get a coin scale (measures to within .1 grams)
like this and use it to keep track of the weight. This is important for health but also can be useful for training. As a pet bird (as opposed to one that is strictly used for shows), you are responsible for keeping it happy/healthy but at the same time some management of weight is not only good for training but also healthy. You definitely don't want to overdo it so learn all about it first and slowly ease your way into it (like over a month+ not overnight).
You are definitely safe leaving the bird without food for 3-6 hour intervals (unless it is sick/injured so don't do it immediately). This is good not only for training (and preventing overeating which isn't a terrible problem in budgies) but it also gives you visual assurance that he's eating. Since he missed food a little during that time, he'll go straight to it when you put it in. This helps you detect when someday something's off and he's not going over to eat.
Another way to tell if he's eating is if he's on a seed diet to look for remaining husks. After a previous feeding blow them off (into garbage bag) and next time you can check again.
12 hours of sleep is a good baseline so I'd recommend covering the cage from PM to AM like 10PM - 10AM, 9-9, or whatever works for you. A bit of routine and consistency helps make their life more manageable both for you and them. Good habits tend to develop. Not a bad idea to shake things up a little from time to time though so they're not absolutely reliant on sameness (not gonna be a huge factor on a budgie but to keep in mind as good operating practice).