The advertising standards authority use a nutritional profiling model. If the food is High in Fat, Sodium, Suger (HFSS) it gets a higher score. Some points are deducted if it is high in fruit, veg or nuts. If the food is above a certain point threshold different advertising rules apply.
This applies to preprocessed food. Not ingredients you would use to prepare your own food.
I don't know about your other questions but some of the other rules are interesting...
You can't use licensed characters or celebrities to advertise to under 16s.
You can't condone or promote unhealthy lifestyle or eating habits. Ie. Eating a massive bucket of ice cream in front of the playstation.
You must not take advantage of a child’s vulnerability by appealing to emotions such as pity, fear, or self-confidence, or by Suggesting that having the advertised product somehow confers superiority, for example making a child more confident, clever, popular, or successful.
You must not present your price in a way that suggests children or their families can easily afford it. "Only". "just". Etc
https://www.gov.uk/government/publications/the-nutrient-profiling-model
Parents should say no, and now this will make it easier for them to do so :)