R – Determine the SharePoint Sites and Webs That A Specified User Can Access Programmatically

You don't need to do anything in code. Based on your description, you are trying to limit access to data on pages, based on their membership of a particular SharePoint group. Break the inheritance from the main site and just configure access for those in that SharePoint group...

I'm guessing you mean how can you ensure the site is indexed immediately?

Generally, crawls are scheduled which means your new site will only be added to the search index after the next crawl is done. So if your incremental crawl happens every hour you may have to wait up to an hour for it to appear in the search index.

However, given that your new sites are being added programatically you could also programatically start an incremental crawl if it is vital for it to start appearing in search results immediately. There are details how to do this in this article.

Update:

The site title and description should be indexed automatically by the next crawl. If this isn't happening, then you don't have a Content Source that covers that site so you need to create/update one to cover the new sites and make sure it has a crawl schedule. If the new sites are created in separate site collections consider putting them on a Managed Path.

In our SharePoint system we have a terrabyte of data with 100,000 site collections and probably 20 new site collections added every day. We only have one content source that points to the root of the site and everything gets indexed automatically.

It sounds like you're missing a content source or a crawl schedule.