show latest posts on front page

I’m making a site for my sister at: https://learntocookathome.co.uk/2009/

I have set it within Settings > Reading so that the home page displays a specific static page, and the posts page is also a specific page.

Currently, only this “blog” page displays the blog entries.

How can I do it so that the home page also displays the latest 3 posts on the home page, underneath the content?

In addition to this, can I get the sidebar’s content to change on my blog page, to show the categories etc?