It is the best practice to add "alt tag" to all images. If there is an option to add "alt tag" you must add them. There are a lot of searches by image. So, you have to have a valid image name and "alt tag"
I am not sure. But I think may try to edit the SEO section for the home page. You need to edit SEO title and description in the main setting(not the page option) for the home page.