1) I never receive messages of theme updates on MONACO theme. (although I have the blue box ticked to be informed of updates) in my downloads section.
2) should I ONLY update Woocommerce thru Monaco theme. because I get independent updates from Woocomerce, but it broke my child theme.
1. Please follow Change Log Update on Themeforest to know about theme update information.
2.WooCommerce had big update in version 3.0.x and we are working on update the theme to compatible with latest version of WooCommerce, please wait a few days, then you can update theme and Woocommerce plugin.