I do not understand, Why Vegan Lifestyle has to be outside of food preparation?!

Veganism is defined in the following quote from the Memorandum of Association, the British Vegan Society (2004), the BVS was founded in 1944 by the creator of the term vegan/veganism, Donald Watson, this definition is based off of his initial definition:
"The word 'veganism' denotes a philosophy and way of living which seeks to exclude — as far as is possible and practical — all forms of exploitation of, and cruelty to, animals for food, clothing or any other purpose; and by extension, promotes the development and use of animal-free alternatives for the benefit of animals, including humans and the environment.
In dietary terms it denotes the practice of dispensing with all products derived wholly or partly from animals."

If you are using definitions that are not based directly from Donald Watson or the Vegan Society's (UK only) than you are probably and likely contributing to the misdefintion of veganism. I prefer the above definition because it is clear and concise and makes good sense for what veganism is.

Veganism is not for health or ecological concerns or any of that (those just happen to be positive effects), it is about protecting and not exploiting animals. There is a dietary component but it is much more than that because animals are suffering in all aspects of life and we must work to do what is practical and possible to eliminate that always working towards eliminating more and more from our lives. Veganism is also about unlearning the speciesist thought most of us have had drilled into our heads. From calling animals "it"s to treating animals are property it is all important to unlearn and work against.

To be vegan is an ongoing process of learning new things and eliminating old things and work to better yourself and those around you while working to end exploitation towards animals. Yes you can also be concerned with health or with the environment but those aren't reasons to be vegan because many of the things we do and use that exploit animals aren't unhealthy or any more harmful too the environment (though some are and effecting the environment can effect animals).

People who are vegans have to be vegan otherwise why call yourself vegan? You (not you specific but you general) don't call yourself a guitarist if you don't play guitar, so the same should apply elsewhere. Don't redefine to fit you, you need to fit the definition. (again noting not talking about you specifically)

vegan because animals are not property

How I define these things:

Vegan diet: avoiding all animal products in the food and drink that you consume.

Vegan lifestyle: as above, but ALSO striving to avoid using other products such as cosmetics, shampoo, toothpaste, clothing, shoes, that contain animal products or have been tested on animals.

When someone says they are ''vegan'', I would take that to mean they follow a vegan lifestyle: not eating any animal products, and also striving to avoid animal products and animal testing in other aspects of their life: clothing etc.

I don't think you are understanding it. What they are saying is all vegans eat vegan (or prepare there food vegan, as they state it) but they may or may not take those vegan beliefs outside of the kitchen. The Vegan lifestyle is making sure not to wear animal hair or leather, using vegan soaps, and beauty products, etc. But some people are only vegan when it comes to food. They may only do it for health reasons or something that doesn't make buying vegan non food products a necessity. It is defining Vegan (the food) separate from Vegan Lifestyle (everything vegan).

My understanding of 'Vegan' is a person who doesn't eat, wear or use any animal products. I think most vegans try to adhere to that. I have never met someone who has a vegan diet but not a vegan lifestyle. To me, strictly speaking, a person who has a vegan diet but not a vegan lifestyle is simply a vegetarian.

That isn't the proper definition.

Vegan: a strict vegetarian; someone who eats no animal or dairy products at all (Princeton Dictionary)

There ya go.

The term for what you're talking about is "raw vegan" or "raw foodist", someone who doesn't cook or prepare their food and eats only raw foods.

EDIT: Her use of the words "vegan" is incorrect. She's a raw foodist.