Can messaging web widget send the message from customer by api?

Hi,

I added messaging web widget on the website and this is my requirement.

1. Customer visit on website's product page and need to ask more info about this product.
2. There is a button named like "Ask more info" or "Talk to support" on the page and when the customer click this button, the below is what we want:
   2.1) The messaging web widget is opened automatically.
   2.2) The system copy that product url and send it to the messaging. It's like the first message sent by the customer so that the agent know what product or the url which the customer stay.
   2.3) If 2.1 - 2.2 is not possible by messaging feature, is there any solution to inform the agent to know what product page which the customer is viewing. e.g. can it update that created ticket with product url as internal note.

Regards,

Pakpoom