How strict transport security header should applied on www subdomain?

I want to add strict transport security header to my website https response with includeSubDomains and preload options. Which would look like this:
> Strict-Transport-Security: max-age=31536000; includeSubDomains; preload

Also, my hosting providers have these redirect flows:

1. http -> https -> https://www.
2. https -> https://www.

That means users always end up at https://www. url.

I noticed that Amazon has a similar redirect flow. See images below.

And it returns hsts header only on www response. Also, I checked hsts preload registration website list and it has registered www.amazon.de but not amazon.de.

So, I have the following questions:

1. If I add hsts with includeSubDomains on www.example.com that means other subdomains like admin.example.com won't be protected? Maybe there are some exceptions for www subdomain?
2. If I register www.example.com to hsts preload registration list, this means that example.com still won't be protected against first request?
3. What is the point of having hsts on www website when you have anyways http->https redirects and base domain(example.com) is not preloaded(amazon example)?

> If I add hsts with includeSubDomains on www.example.com that means other subdomains like admin.example.com won't be protected?

Yes. From RFC 6797:

> 6.1.2. The includeSubDomains Directive
>
> The OPTIONAL "includeSubDomains" directive is a valueless directive
which, if present (i.e., it is "asserted"), signals the UA that the
HSTS Policy applies to this HSTS Host as well as any subdomains of
the host's domain name.

There are no special rules for the www subdomain.

> If I register www.example.com to hsts preload registration list, this means that example.com still won't be protected against first request?

You can only register example.com, not www.example.com - see for yourself. Generally, you can only register an etld+1.

You might be able to get an exception if you're a very large company. See the Chromium preload file - there are special rules for Google, Amazon and a few others, but everyone else can only preload whole domains.

> What is the point of having hsts on www website when you have anyways http->https redirects and base domain(example.com) is not preloaded(amazon example)?

This means that a browsers first request to amazon.com is insecure, but after the first request the browser will remember the HSTS header and subsequent requests to amazon.com will be secure. If they had the redirect but no HSTS, every request to amazon.com would be insecure.