Hi there,
Since your website is already running on WordPress, it should be no problem to add WooCommerce to it! WooCommerce is just a plugin for WordPress which adds eCommerce functionality to the site. (I’d recommend taking a backup of the site before installing and setting things up, just in case).
For your “Escrow payment system”, if you were looking to accept payments from customers, that should be possible.
You would need to setup a payment gateway for processing transactions:
https://woocommerce.com/product-category/woocommerce-extensions/payment-gateways/
Then you could create manual orders for your customers’ payments, and send the invoices to them. There’s information about creating Manual orders in WooCommerce here:
https://docs.woocommerce.com/document/managing-orders/#section-16
There’s more information about getting started with WooCommerce available here:
https://docs.woocommerce.com/documentation/plugins/woocommerce/getting-started/
Finally, if you wanted customers to be able to enter the amount they want to pay (instead of creating manual orders), then our Name Your Price extension could help with that. It would allow customers to enter the amount they want to pay, then proceed to Checkout and process the payment:
https://woocommerce.com/products/name-your-price/
I hope that helps!