Hello, I have a question. For some reason, when the proxy is enabled, the program falsely detects pixhost, pimpandhost, and imagetwist photohost links as "dead" (Possibly dead/offline. Host responded with http code: 407). This happens only with the specified hosts, and everything else is ok.
Is the problem with the proxy or something else? Everything worked fine without the proxy.

407 is a proxy error, you might have saved incorrect user / password for that proxy or they don't want to accept those logins details (issue in the proxy) or the hosts are blocking that proxy.

The links are not accessible at all so the program thinks they are dead.

If you really want you can add 407 code in "HOSTS" -> select host -> under "Ignore codes", enter 407 -> press "Update" button, but then basically all links won't be checked at all (since proxy is not working correctly).

Strangely, this proxy is also in my browser and there are no problems with these hosts. The images of these hosts are also displayed in the program, but for some reason the links are still marked in red.

Do this: "Help" menu (at the top) -> "Support" -> "Compress" -> send me the file which it opens.

Will review your settings.