Assembled products are physical products you manage stock quantities.  Like you sell computers assembled from the motherboard, RAM, CPU, and SSD, the computer is an Assembled product. When assembling, you increase (adjust inventory) the quantity on the computer and decrease the quantity of the parts. So the quantities of the sub-items will not change when you sell the Assembled product (the computer, main SKU) unless you turn on the switch 101 (auto-assemble) in the store settings. Prices, quantities and taxes are calculated based on the Assembled product (the main SKU, not sub-items).

Bundled products (in POS only) are virtual products you don’t manage stock quantities on bundle (The main SKU) products but manage stock quantities on individual products. Like you sell a camera package including body, lens and warranty services, the package is also called Bundle. You don’t track stock quantities on the bundle, but you track quantities on the body and lens. When you sell the bundle, the POS will auto add body and lens (all sub-items) to sell, show package prices, and hide body and lens prices. Taxes and quantities are calculated based on the sub-items.

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.