Insert 'add to cart' button in new page

It’s not copy-and-paste code, but I think you can do this https://docs.woothemes.com/wc-apidocs/class-WC_Cart.html#_add_to_cart

Yeah, there’s a bunch of available shortcodes
https://docs.woothemes.com/document/woocommerce-shortcodes/

Depending on how much detail you want displayed, you could do
[product id=”99″]
or
[add_to_cart id=”99″]

with 99 being the product id number.