One simple way to do this (without having to create a child theme) is to hide these values by adding custom CSS. You can add the CSS at Appearance > Theme Options > Layout > Custom CSS.
The date/author meta information for individual posts has a class of “entry-meta”, so this CSS will hide it:
.entry-meta { display: none; }
As I’m using pinboard, the meta information doesn’t appear on the home page, so I can’t give you specific CSS for that. But if you view the page source you should find a class being applied to the meta information on the home page. You could try suppressing it in a similar way.
.[class name goes here] { display: none; }
This could have unintended consequences of hiding information on other pages, so as with any custom CSS be sure to test it thoroughly.
Best of luck.
Andy