enqueue jQuery into the footer

Sure. Set the fifth parameter of wp_enqueue_script or wp_register_script as true, and that script will be placed in the footer.

For example, your line

wp_register_script('jquery', ("http://ajax.googleapis.com/ajax/libs/jquery/1/jquery.min.js"), false, '1.7.1');

should be

wp_register_script('jquery', ("http://ajax.googleapis.com/ajax/libs/jquery/1/jquery.min.js"), false, '1.7.1', true);

And if you ever don’t need/want to specify a version number, just set the fourth parameter to false.

More info: http://codex.wordpress.org/Function_Reference/wp_register_script

By the way, to make sure you’re avoiding any conflicts, I would recommend you prefix the names of all your custom scripts.