I would like to know how I can hide the tags from showing at the bottom of my posts. Also, If I do this, will it affect search engine rankings?
You can hide the post meta for posts in the Twenty Eleven theme by adding the following CSS to your Appearance → Custom Design → CSS editor:
Note that there is not a way to split out just the tabs because of the way the HTML is structured.
Regarding search engines, no one can really predict that except the search engines themselves of course. I can tell you my opinion which is that I think the post title and content matter much more than a long list of tabs at the bottom of a post.