Yes, all of the aspects of our embeddings can be changed in any way you like.
The CSS code would be used in all cases, however you could really even do it through JS if that was needed.
Now if you tell me the theme you are using I could help you with the exact class that you would use for this (some classes change based on your theme name and color.
In terms of knowing when the localplayback is available or not, there is no option at this time. With that said, you could listen for "ready_to_play" event as that would tell you when the video can be played. This will fire before the playing event (when someone actually starts the playback).
If the video is still uploading when the event telling you that video is ready to play fires the video is available for local playback.
Now with all of that said, you could really change the text or background of the embedding notification and have it styled in such a way that it is easy to see what it says, regardless of the background.
Actually some of our themes have this type of implementation already so I do suggest checking out all of our themes to see what looks best for you if you did not do so before :)
Recorder themes: https://ziggeo.com/features/video-recorder-themes/
Player themes: https://ziggeo.com/features/video-player-themes/