How do i use the use the wooCommerce functions in a wordpress plugin?

Question

I believe, the hook is called differently

add_filter( 'manage_edit-product_columns', ... )

The ‘woocommerce_edit_product_columns’ is not a hook name, but a function name in WC 2.0

As for the access to global $woocommerce – as long as the WooCommerce plugin is loaded, it’s available. If, however, your plugin is loaded before WooCommerce (alphabetically), then you can should do something within a function hooked to ‘plugins_loaded’.