The problem with website box is the use of an iframe so the content can be bigger than the display area. Into the advanced part of the plugin you can resize the content area for tablet/mobile.
On PC (Change the width of the browser) is OK, but in mobile/tablet not. I try change all parameters in advance section without result (I cant set "Max scrollable width for mobile/tablet devices" to 320px because on tablet looks awful). Website plugin is uncompatible with responsive pages in mobile/tablet.
Yes not fully responsive. It's due to the limits of the iframe under mobile devices. For browsers/os security reasons you can't get the internal size of the content loaded into the iframe. So the advanced parameters of the plugin which are quite limited, you're right, are here to bypass these limitations with "hardcoded" values.
You can also use the javacript call action to call a JS function into the HTML page and add your own HTML box into the HTML page with it's JS links which will be caled by the JS function.