Hi,
I suggest talk with expert in your city/country about SEO in Joomla, take a few lessons. You have to know the basics if you want to build sites for client$ or yourself. Don't get me wrong, it's honest advice, like with Music Lessons.
ad 1) Now your home page has:
<title>Home</title>
weak :/ Correct that in Menu item, separetly for each menu item. This is MUST HAVE (!)
ad 2) Google index what it wants, sometimes something that we don't want to, even a hidden content, the same in for all CMS (!). ALT - is for accessibility purposes mostly, but Google can index that too.
Ad 3) Google take "first" image that it see on the HTML code, sometimes it can be random one. That's why it's important to use Open Graph and Google Structured Data (Schema.org) to have more control - that feature can be from extra components.