This is a very broad question. I suggest asking a series of more focussed questions to get specific answers to the various problems you are faced with. Anyway here are some ideas for you...
There are a few things going on here. You need to process a URL, convert that URL into something printable (probably a PDF file) and then automate the printing of it on your Epson printer.
Software is available to automatically print documents that appear in a folder on your network, so you can use that kind of thing to print PDFs. Google "automatically print pdf files in folder" and find something that will work with your printer.
For the other problem of getting something printable from a URL, I presume you do not wish to code up your own solution, so perhaps you can find an App to render HTML to PDF and save the file to a folder or network location. Have a look at IFTT, there is an app there called Pocket, that can convert a URL to PDF and save it to Google Drive. If you link Google Drive to the folder on your network that automatically prints documents, perhaps you will have a solution!
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