If I am an participant(not host) can I register attendance of the meeting?

No, you would need to be a host or co-host in order to get that information.

No you can't download the attendance register unless you are a host or a co host.

For assistant you don't need have one licence, only if you are host. Now, if you want begin a meeting, you need a license, but if the host go out the meeting continue anyway. I hope for clear your ask.

It depends on the setting that the host set up. It also depends if it’s a webinar license or a regular license. If it’s a webinar license they may have you register, but it’s at the creator or the webinars discretion.

I am not sure that this is possible. You can see as a user who attends, but downloading information or anything from the management view is not possible for users.