( I need a long detailed answer.)

"What challenges might a vegan or vegetarian restaurant face when it comes to stocks and sauces that a non-vegan or non-vegetarian restaurant would not? How can these challenges be overcome? Do you believe that vegan or vegetarian stock, soup, or sauce can compete with stock, soup, or sauce made with animal parts? Explain."

They may loose market for the non vegetarian customers.
They have to be extra creative with their dishes to make them taste and look tempting.
The variety of ingredients that they can make use of while cooking meals is reduced considerably, since they can not make use of anything that comes from animals.

2- Following are some of the ways through which vegan restaurants can get over these challenges;

Vegetarian restaurants can offer something for the non vegetarian customers as well to cover the entire consumer base.
They can come up with interesting and new recipes utilizing the vast variety of fruits and vegetables available in the market.
They can hire specialized vegan chefs to increase the vegan menu.
Since they cannot use anything that comes from animals, they can use vegan products to replicate the same flavor. For example, watermelon steaks replicate a beef steak in looks and in flavor.

3- There is no comparison between the stocks and sauces that are made from simmering body parts of animals like bones and meat scrap, and stocks that are made from vegetables. But if certain vegetables and spices are simmered together, they can replicate the flavor quite closely.

The trick is to use the right combination of vegetables and spices for the desired result. For example vegetables like onions, carrots, celery stalks, sprigs, fresh thyme, bay leaf, small bunch fresh parsley, black peppercorns and etc make a mouth watering broth and soup base.