The health permit is (if it is required) is required by anyone who works with food or thinks about food, regarless of ownership. Some states (mine) does require a more advance food safety class unless you can prove that you are fairly knowledgable about food safey.
Now about diplomas. No of course not. However if you are applying for a loan from a bank you will have to prove that you have sufficiant amount of training and experience to make the enterprise work and a diploma is one way of showing some. Some insurance companies might also care.
Is this purely a academic question? Unless you have money to burn, (or are just expanding here in the US)I would have to suggest that if you are asking the question, that you should spend some more time in the industry/culture before embarking on your own. Talent and skill in baking/cooking is only about 10% of what it takes to surrive and succed. Even pure business is not enough. It is easy to fail when you are unfamiliar with the nuances and culture of the environment that you operating in. I am not trying to be mean. I am the biggest advocate for business ownership, but I want people to succeed. Opening with a store front is very different from working from your home in many aspects
"Just can't wait to get on the road again."