Products come out at Products then All Products then Export, where an admin picks the columns, the product types and the categories, ticks custom meta fields if wanted, then clicks Generate CSV and the browser downloads the file; a subset comes out by ticking rows in the list and clicking Export X selected. Order and revenue history comes out of the reports: open Analytics, pick a report such as Orders or Revenue, and click Download at the top right of the table. A report that fits one screen, 25 rows by default, downloads straight away, and anything longer runs as a background job, after which WooCommerce emails a download link to the address on the WordPress account of the admin who started it.
What it holds
Orders with their line items, customer records, products and variations, coupons.
Find the size
WooCommerce prints the figure itself: WooCommerce then Status then System status gives Total Database Size, Database Data Size and Database Index Size, then every table with its data and index size in MB, and the Post Type Counts section under it counts the shop_order and product rows. Quote the total database size and the shop_order count.
What to enter on the form
WooCommerce in GB, and the year your company started using it. Seller form