Using Specific Cat-Links On Main Page

With respect to the 2nd point, the first and last items on the meta line have negative top margins, so

span.byline {
    position: relative;
    top: -7px;
    margin-right: 10px;
}

will adjust that.

To add or override CSS: use the “Additional CSS” option in the customizer. https://codex.wordpress.org/CSS#Custom_CSS_in_WordPress

Learn to use the Chrome Developer Tools or Firefox Developer Tools to help you see and test changes to your CSS.

With respect to the first item, you may have to make a child theme to change that. I recommend asking at https://wordpress.org/support/theme/areview#new-post so the theme’s developers and support community can help you with this.

Try this:

.home span.byline {
    position: relative;
    top: -7px;
    margin-right: 10px;
}

That should affect only the home page.