To answer the second question, yes, you can customize the Okta hosted login page on an application by application basis. On the Okta hosted widget, you can detect which application is being used in an SP initiated flow, and use that to control the logic about how your widget is modified.
More details about this in our documentation about how to Style the Okta-hosted Widget and in this post where I offered an example for how to customize the page for OIDC apps and/or SAML apps