Search engines will pick up your links naturally, provided that your pages are crawlable. If you use certain techniques such as writing text onto the page using JavaScript document.write(), then your pages won't be crawlable.

It can take weeks for new things to show up, especially in Google.

It is often said that search engines tend to crawl "shallowly", that top level folders and files are crawled more often and thoroughly than deeper files. If that's so, then they're doing a pretty bad job of crawling!

Someone else can comment on whether the format you show poses a problem for search engines. It's possible to rewrite your URLs to a more supposedly "search engine friendly" format, but I don't know if it's necessary.

You would add your own site pages to your sitemap, but there's no place where you can or should report your links to other sites.