Hi again @tekgirlymama Looks like some of my answers were incorrect. Sorry about that!
Here are answers to each of your questions:
Question: Will a full page overlay be seen by seqrch engines or is there a way to hide it?
Answer: Yes, the page overlay will be visible to search engines. The content from the overlay will live in the page’s HTML.
Question: What is the SEO impact if it’s non-closable full page [so it looks like page content]?
Answer: If it’s full-page and non closable, then it’s likely Google will punish the rankings in search results, but this only applies to mobile. We’re wondering what the use case is for a full screen popup that isn’t closable — would you be trying to think of a way to change the page’s content? If so, why not redirect users to a normal (non-pop-up) page with the content? That’s better for SEO and user experience.
Question: Can I embed another website’s page in there or a lander from same site?
Answer: There’s a line in the code preventing iFrames:
$content = apply_filters( 'the_content', get_post_field( 'post_content', $this->config->current_id ) );
Wordpress by default strips iframes when filtering the_content for security reasons. So it’d be difficult to embed another website’s page.