Yes, you can easily embed Youtube videos into your blog posts as well as pictures. All you need is the EMBED code you get by clicking the share button on your video in YouTube. Copy and paste that code in your blog and voila - video in your post.
You can also FEATURE any blog post you want on the home page of your website - Like this one. When you write your post, there is a check box for "featured". Just check it and your post will show both HERE in your blog list AND on your front page. It's that simple! Go Ahead and click back to HOME now and you'll see this post is featured there too.