Sell Normal Products and Events in one website

That is not supported.
Are you sure that you want to use entry custom fields ?
With entry custom fields, you can only have one event form so if you sell several of them, I would recommend another approach since you won't be able to sell several of them at the same time.
Now, without knowing the details of what you want to do, I can't say if it might or might not be suitable, but I would recommend to create products for your events and then use custom fields of the table "item" in order to have the users enter information for each product (event). Then, you would be able to have both types of products in the cart.