Assembled products are physical products you manage stock quantities. Like you sell computers assembled from the motherboard, RAM, CPU, SSD, etc. When assembling, you increase the quantity on the computer and decrease the quantity of the parts. So the quantities of the parts will not change when you sell the computer, they will be changed if you assemble or disassemble or sell parts individually.

Bundled products (in POS only) are virtual products you don’t manage stock quantities on parent/bundle products but manage stock quantities on individual products. Like you sell a camera package including body and lens. You don’t track stock quantities on the package, but you track quantities on the body and lens. When you sell the package, the POS will auto add body and lens (all children products) to sell, and show package price and hide body and lens prices.

Grouped products (in WooCommerce only) are virtual products listed on WooCommerce. Nikon Camera body and lens can be in the Nikon Cameras group. Customers can buy a body or lens individually from a group (Nikon Cameras group) of items.

So the answers to your questions:
1. the simple(child) product stock quantity will not be updated.
2. Bundled products cannot be published to WooCommerce. Assembled products will be published to WooCommerce as simple products.