1) This is a Javascript application. So, the calendar data transfer occurs between the user's web browser, and the calendar server itself; in your case, between whatever web browser you use, and your Nextcloud server. When an application on one server wants your browser to access resources on another server, this presents a major security problem. This is known as XSS, or Cross-Site Scripting. All major web browsers prohibit this today. Firefox has a Developer under Settings -> Web Developer -> Web Console. Chrome has the same thing under Tools -> Developer Tools. These consoles will display XSS, and any other, errors.
2) A Proxy Server is just another potential work-around around for this problem. In the plugin configuration, you would program in your local webserver address for the CalDAV server address. Your proxy server forwards the requests to the actual CalDAV (NextCloud) server. So to your end-user Web Browser, everything looks like its coming and going to the same server (Roundcube).
3) If you wish to post a question here requesting configuration information, then do so. But as you can see, this is a new plugin that doesn't have a lot of active installations yet. You will probably get better support from Synology. Synology is a commercial product; you should expect to get good service from them.
4) Your expectations are unreasonable. The developer's job is to make a working plugin with Roundcube. That is all. It is not his/her job to tell you how to configure it for OwnCloud, PureCloud, NextCloud, or WhoEversCloud. It is not his/her job to tell you how to configure it for Apache 2.2, Apache 2.4, Apache Whatever, NGINX, LightHTTP, Node.js, IIS, or anything else. The plug-in works fine. It is very good. There is no reason to insult the developer.