Does the aluminum case pose any risk to your health like Alzheimer’s

You are not eating the Apple Watch, just wearing it.

This will tell you the materials used in the Apple Watch

Wearing your Apple Watch - Apple Support

Prices vary for several reasons.

• GPS only vs Cellular. The Cellular generally costs about $100 U.S. more than the GPS only because it includes additional cellular electronics.
• Watch band. The basic watch band does not add much to the cost, but if you decide to get one of the fancy watch bands, that will cost you more.
• Special Editions, branded by "Nike", or "Hermes", etc... you paying for the name (and some additional features only available with that model).
• The case. The Aluminum case is the least expensive case. Stainless Steel with a sapphire screen is more expensive. The Apple Watch Ultra has a titanium case, is rated for scuba diving, ultra sports, etc.... and has a price to match the higher specs.

But you eat the food cooked in the aluminum frying pan that gets scraped with other objects that can be transferred to the food.

You do not mix food with the Apple Watch. Or at least, that is not recommended.

If you are really concerned about aluminum touching your wrist, either avoid the Apple Watch, or get a model that does not use aluminum.

You do realize that your skin in made of pores right? Your pores allow toxins to enter through and ultimately get inside your body. Wearing an aluminum (which is harmful) watch all day, can possibly cause damage.

don't eat the aluminum case