You can either hide the tags on a post-by-post basis using the toggle in the "Shape 5 Options" area (you may need to enable it by clicking the "Screen Options" tab in the top right of the page/post edit screen), or you can add the following CSS to the end of the style.css file for the theme.
.tag-links {display:none;}
That will hide the tags on all pages, but leave them in the code where Google and other search indexers can find them.
As for the "Older Posts" thing.. That capability is already built into the theme. Any page listing multiple posts should automatically add the back/forward link when the category it lists has more posts than allowed on a single page.