How can I commit changes to a theme? I worked on Omega-7.x-3.0-alpha1 and added some fixes to fluid style sheets in rtl mode.

How can I commit them to the drupal.org repository?
Unless you are one of the maintainers or have been explicitly granted write access to the repository, you will not be able to push your commits to the "official" branches.

The recommended route to contribute is the following:


Checkout the git repository for the correct branch (instructions here)
Create  patch with your changes (instructions in the above link)
Search for a relevent issue or create a new one in the project's issue tracker on Drupal.org
Submit the patch in the issue