It is a problem with OpenSong in combination with Windows Creator. Is it not an HDMI to VGA problem, although it could be that it effects you less when your screen is at low(er) VGA resolution.
You are probably right about the GDI rendering. The most recent releases were build with a Xojo release that did not support this yet. Support is only available as of Xojo 2016r4 (released December 2016). As far as I know, none of the developer has a valid license to be able to use that version for a release. But maybe I am mistaken.
OpenSong cannot 'do' HTML as in 'render it'. In a custom command, you can execute a Java program that shows something to the screen. Similarly, it can start a browser that shows HTML. In the development version (not released yet), a feature is added to enable external rendering. This means that OpenSong will handle everything, except for rendering of the slides. This (generation of the image) can be delegated to an external program. This will not support display of video, but you can use it to show...
OpenSong presentation delay
Have a look at this support request that addresses this problem: https://sourceforge.net/p/opensong/support-requests/179/ (after windows 10 creators update the presentation of verse on 2. monitor/beamer need 5 seconds).
Which exe are you specifically talking about? For VLC, OpenSong knows how to handle it, but it has no knowledge on just any exe. It just runs the command you specify. If the exe does have a way to control on which screen it plays by means of a parameter, you can add that.
There is no older function of OpenSong that includes newer changes for the CCLI website changes. This can be fixed by someone that has a CCLI license and is willing to contribute to the codebase of OpenSong. As far as I know, none of the current developers have a CCLI license or other means of access to SongSelect. Although ... a quick checks seems to suggest that it is possible to get a free account (without the need for a CCLI license) to access Public Domain songs. That might enable fixing the...
Mentioning or refering to OpenSong is never a problem. If you create a group for OpenSong users with the name 'opensong' that is not a problem. See for example a French site: https://opensong.fr/ or a Dutch user group: https://groups.google.com/forum/#!forum/opensong