How do I make a custom header?

I tried making a custom header using widgets or customize theme but it doesn’t have any option to customize it. I tried the Blockspare plugin but that can’t import to the website. I also used the Elespare plugin and I got the header template that looks the same as the one in the thumbnails.

At the top I wanted to add the extra header that has the date and time and the social media icons. When I added it I couldn’t choose for it to only display on the homepage.

I tried adding the header template provided.

Below is what it looks like originally.

I’m not sure how to add it on, or am I doing something wrong and there is a better way of doing it.

Thanks