Posts Link to Wrong URL

I have two questions, but the first is the most important. On my home page, chelslivin.com there are three short posts currently. The posts have a title that link to what should be the category page they are assigned to. Instead, they ALL link to a page /diy-wedding that does not exist. So nothing I post is fully readable. Help please!

The second part of this question…is there any way to show the full posts on the home page? Thanks on both.