svenknebel.de / reply

Yes, totally trusting the claimed url is a potential issue, and e.g. my own webmention handling code only allows it for a whitelist of trusted services like brid.gyi, where I know they intentionally pretend to be a different domain. I'm not involved with the Wordpress plugins and their development, so I don't know what rules those follow here.

Regarding the mentions vs replies, they have to be clearly distinguishable to avoid misunderstandings (see e.g. this example from the Indieweb wiki for how it can go badly), and since it isn’t clear how important a mention is, many prefer to have them displayed as compact as possible. That said, if you prefer it differently I’m sure the plugin devs will add an option for you or tell you what to modify if you ask them for help.

From my understanding, neither the Webmention nor the Semantic Linkback plugins are responsible for setting up microformats markup for your page, they merely add some aspects of it that are part of their responsibilities. Ideally, this is handled by the theme, and there is the microformats plugin which attempts as good as it can to inject the correct markup, but is limited in what it can do. The Indieweb chatrooms (available via IRC, Slack or a web interface) are probabably the best way to get help with that. I'm happy to help figure out what's wrong with markup, but don't know enough about Wordpress to directly help fixing it.

Lot's of things going on here, but I think I figured them all out.

missing avatar

Frank’s site is only served over HTTP, not HTTPS. In <img src="">, that’s fine and only creates a warning in the browser, but in your comment display it is included in <img srcset="">. Here, browsers do not accept mixed content, so the image is blocked and not shown. This is also why there is no default avatar: the avatar was found and is requested in the HTML, but the browser refuses to load it.

link to news.indieweb.org

The odd bit is that indieweb.org address is not mentioned in the source of Frank’s page.
That’s not true, and the problem in this case. There’s a <a href="https://news.indieweb.org/nl" class="u-syndication"></a> as the only top-level link inside his post, and no explicit url property set. This causes the microformats parser to assume that this link points to the canonical location of the post, and it is thus used for comment display. This seems like a problem with the microformats specification, and I'll follow up on it there, but for now the easy fix would be for Frank’s posts to mark up their permalink, e.g. by adding a class="u-url" to the link on the headline.

absence of content in comments

This is intentional. Frank’s post only mentions your post (=includes a link to it), it is not marked up as an explicit reply. Only replies are shown with content, since for mentions this is often misleading.
One reason to have permalinks for comments is that you can reliably send Webmentions from them. Another one might be comment pagination, where you otherwise need JS to find the right page?