The “latest post” will not show any links. All links and formatting are stripped from the excerpt that is shown.
On the featured posts (sticky) if you have the home page set to show excerpts at appearance > theme options then again the formatting and links are stripped out. If you have the home page set to show full posts at appearance > theme options > General (show full content home), then the links and formatting will show. You can then manually insert the read more tag to shorten the posts if you wish.