恥ずかしいからカメラはオフでって英語でなんて言うの？

Well, there is no obligation for you to give an explanation to your teacher. Having the camera turned off is a valid option and it's taken up by great numbers of students every day. So phrase 1 is fine. However, if you prefer to give a reason, better would be to say you are just relaxing, rather than embarrassed. That is quite enough explanation. If you feel like a making a joke of it, phrase 3, may be suitable.

If someone is shy it means that they are nervous and uncomfortable with other people.In this case you may be too shy to speak to the teacher in English and you can gain some confidence if you speak while your camera is off. For example:Children are often shy of people they don't know.

If you are asked whether you want to have the camera on then you could say 'I would rather have/keep my camera off' or 'If you don't mind I would rather have my camera off' by adding I'm a little shy/embarassed you are explaining why

Native speakers will say like this: “I'd like to keep the camera off, as I'm shy”. There are lots of other ways to say it, but this one is the most accurate and most commonly used. Here is an example on how to use this in a conversation: A: You can turn on your camera if you want to. B: I'd like to keep the camera off. I'm quite shy.

In order to politely explain that you would personally prefer to keep the camera off due to embarrassment, you could state "I would rather leave the camera off. I can be quite shy". You could also politely say this without mentioning your embarrassment by stating "Sorry, I would rather not turn the camera on today".