@Muzzy only sales orders are created with the standard woocommerce integration and no, sales invoices or payment entries are not created if/when payment is completed on the woocommerce/ecommerce site.
To your second question, there’s no 2-way sync for stocks. The source of truth for stocks is woocommerce and it does not take into account stock values in ERPNext before creating sales orders either. What’s worse, woocommerce tends to create it’s own items when syncing sales orders to ERPNext so even if you already have the item created in ERPNext woocommerce ignores it and creates its own.
The woocommerce connector developed by @lasalesi discussed in this thread is promising but so far i haven’t seen anyone who has got it to work. I have tested it extensively but i can’t seem to get it to sync stock to woocommerce and there isn’t much answer why.