How to Remove "This entry was posted " in Twenty Twelve theme

similar to what you have done already for the home page ( https://www.ads-software.com/support/topic/how-to-remove-this-entry-was-posted-in-twenty-twelve-theme?replies=9 ):

.category .entry-meta {
    display: none;
}

.category .comments-link {
    display: none;
}

.home and .category resp are archive specific outputs of the body_class() function on the body tag; https://codex.www.ads-software.com/Function_Reference/body_class

for generally all archives, use .archive instead of .category in the CSS codes

How to remove the “line” between the posts in Category Archives Page & Bottom of the Single Post