Simlpe Product

Are you trying to set up an External/Affiliate product? If so, see how to do that here:

https://docs.woocommerce.com/document/managing-products/#section-7

If you have an affiliate link, you’ll want to make sure you insert the proper link into the product editor in order to have the purchase tracked.

I am asking will I receive commission if I set Simple Product as product type?

I only need to know is Simple Product also for amazon affiliates or is it for personal products?
It confuses me that I have checkout on my website and not on amazon official website.

Simple products are for personal products. If the product is a simple product – the customer will be purchasing it on your website. The money will go straight to you.

External/Affiliate products are simply a link to external sites where the customer then buys the product using your affiliate link.

Is it possible to create a shopping cart on my website and then checkout on external site?

Not really. You typically can’t send a whole cart to another site.

How did he managed to do it – https://www.youtube.com/watch?v=CoEMb3wRTDY
Look at 13:00
And I managed myself to do it without any additional plugins but don’t remember how.

He is using a plugin: https://codecanyon.net/item/woocommerce-amazon-affiliates-wordpress-plugin/

I don’t know how you managed to do it without the plugin.

I used the light version of that plugin, thought that it implies with woocommerce, but I realize now that woocommerce can be used without amazon… never mind… do you know how can I do it with light version of that plugin?

Maybe if I delete checkout page it will automatically go to amazon.

Maybe best to ask the author since this is not WooCommerce core.