Hide subscription button on some pages

Is it possible to hide the button on some page?

It isn’t currently possible to hide the button on some pages.

How can I make custom notifications?

You can send a custom notification in the ‘Send a custom push notification’ page in the Tools section (wp-admin/tools.php?page=web-push-tools).

Is it possible to display the subscriptiom Box automatic when a New vistor is coming?

Do you want to ask permission to send notifications to the user as soon as he visits the site?
It is possible, you just need to modify the “Automatic prompting” option. Note that it is highly unsuggested to do this, because most users will dismiss the prompt if it appears as soon as the page is loaded even if they didn’t do anything.