For example, in view_all_bug_page.php HTML code:
<img border="0" width="16" height="16" src="http://mydomain.ru/images/update.png" ...

And really need source:
<img border="0" width="16" height="16" src="httpS://mydomain.ru/images/update.png"

In view_all_bug_page.php HTML code:
<img src="http://mydomain.ru/images/priority_1.gif" alt=""

"src" must be "httpS://mydomain.ru/images/priority_1.gif"

<link rel="stylesheet" type="text/css" href="http://my.fl34.ru/css/default.css" />

<a href="http://mydomain.ru/issues_rss.php?username=admin&amp;key=94167dcghrhrch53537&amp;project_id=1">

When I run mantis from behind a public proxy and forward https -> http, I experience a similar problem to what you are observing. For me this is related to issue# 0006134. I want to be able to have users access mantis securely from a public address https://mantis.mydomain.com and developers access mantis on the internal network at http://localserver/

To get things to work properly I simply tweaked the config_defaults_inc.php with the following:

$t_protocol = 'http';
if ( isset( $_SERVER['HTTP_X_FORWARDED_PROTO'] ) ) { // Support ProxyPass
$t_protocol= $_SERVER['HTTP_X_FORWARDED_PROTO'];
} else if ( isset( $_SERVER['HTTPS'] ) && ( strtolower( $_SERVER['HTTPS'] ) != 'off' ) ) {
$t_protocol = 'https';
}

This has the system working in both scenarios. Would be great if this tweak could make its way into the next release.

This has been fixed for a long time.