How to change "Bets Center" text

To change this text, please edit file /templates/hot_betting/index.php in plain text editor and change text in this line (it's around line 316):

<div class="tabs_heading"><span>Bets</span> Center</div>

Text between <span> and </span> will be shown as black.

How to change Tab text and how to put Bets Center under the Featured News?

that is simple article with HTML content. So to move title and change tab headers you need to edit that article, but that is HTML recpectfull to jQuery tabs function so I recommend you to do all changes in HTML mode. Tabs headers are in LI tags at begining of tabs container.