Were the domes of Al-Baqi' against Sharia? Is it permissible to leave graves unmarked and exposed to being trodden upon? Has it been confirmed that these graves belong to the Companions?

It is not permissible to construct domes over graves. The Sunnah is for the grave to be raised about a handspan and to be humped, and not raised more than that. This is based on the Prophet's (peace be upon him) saying to Ali: "Do not leave any image without effacing it, nor any raised grave without leveling it." He also forbade plastering graves, building over them, and sitting on them. It is permissible to mark a grave with a stone or pebbles. As for the graves of the Companions, many of them are known, as mentioned in some specialized writings about Al-Baqi'.