Force dark was only added as a (hidden) option on Android 10 and above. If you want to change the theme of apps prior to Android 10, you may wish to use a Substratum theme.
Since the final beta of Android 10, the force dark property (debug.hwui.force_dark) is only writable with root or with the shell UID (which adb shell and therefore Shizuku runs with).
DarQ uses a hidden API only accessible to privileged code (IActivityManager.registerProcessObserver), which allows it to know when an app is opened or closed without an Accessibility Service.
For some reason, in the final beta of Android 10, a requirement was added to force dark to make it only work when the system dark theme is enabled. A workaround has not been found (and may not even exist) for this, so it is required for DarQ to work too.
Short answer: No.
Long answer: Force dark is able to invert light colours to dark, and dark text and icons to light, but is not perfect. Gradients are often broken (such as in Facebook and Facebook Messenger), and sometimes regular images get caught in the crossfire and are inverted too, making them look incorrect. As force dark is literally just a property for DarQ to change, there's no way to configure or tweak its sensitivity and so apps can't be fixed. In a way, that's why DarQ even exists - so you can enable force dark on the apps that do work, and leave it disabled for those that don't, or that already have a dark theme.
Please do not pester app developers to fix apps with force dark enabled. Force dark is a not normally meant as a user-facing tool, it is meant for developers. If enough developers complain to Google about users pestering for fixes with force dark enabled, it may be removed from a future release of Android, preventing DarQ from working at all.
Sometimes an app launches too quickly for force dark to be applied. You may have luck closing and reopening the app, or opening and closing recent apps.
During testing; LinkedIn, Facebook and Google Opinion Rewards were found to be usable with force dark enabled. Plenty more will work too, it's up to you to experiment and see what works.
No. Apps are able to disable force dark in code, so Xposed is the only way to prevent that.
This appears to be a bug in Android, and as force dark is a developer option, may not be fixed. It may be possible to fix it with DarQ, and this is being investigated
No. There is no customisation with force dark, so you cannot change the colours.
DarQ is not on the Play Store, as it uses hidden APIs, which Google does not like. DarQ is instead available on GitHub, and will automatically check for updates when launched. If you would like to check manually, use the GitHub link on the main page of DarQ, and follow the "Releases" link.