Q2 : From the picture What are api1-2-3? they are api proxy?
Yes, in the image api1 = apiproxy (API_Proxy_1 = api1)
Q1 : Why we map api resource into product.
api resource is in api proxy. why not map api proxy into product?
because I think api proxy is in api product.
We define multiple API Resources in API Proxies. In Products we define API Resources. By doing this, you can control control access to the API resources in an API product. For example, you can bundle api resources that can be accessed by internal developers only in one product and create another product for paying customers only.
Assume there is only one proxy with 3 api resources(/foo, /bar, /foobar). Create a product(internalProduct) with all three resources for internal developers.
For external customer you want to give access to only /foobar resource. In that case you can create another product(customerProduct) and only add /foobar resource.
So now the credentials(API key and secret) of customerProduct will only have access to /foobar resource.