The following will hide the date/meta data from your home page only.
.home .entry-meta {
display: none;
}
To create a static front page, you would first create the page and add the content (your image and text) and then go to Settings > Reading in your dashboard and set that page as the “static front page”. If you are going to have a blog page, create that page and publish it and then set that as your “Posts Page”. If you aren’t going to have a blog, then simply don’t create the page and leave that selection as is.
Since your site is hosted at WordPress.com, the correct forums are at https://en.forums.wordpress.com. For CSS and Customization questions, you can post in the CSS forum there and staff or one of our talented volunteer would be more than happy to help you out with your questions. These forums are for those with self-hosted WordPress installations and the solutions and options available to each are different.