Is it valid to pray four continuous rak'ahs with the intention of the Sunnah prayer before Dhuhr (the mid-day prayer), with one taslim at the end? Are the hadiths that mention its virtue for reciting the Qur'an authentic? And is it necessary to wait for the verse to end before stopping the Qur'an recitation?

It is best to pray the two rak'ahs of the pre-Dhuhr regular sunnah prayer with one tasleem (i.e., as two separate rak'ahs, each ending with a tasleem). However, it is permissible to pray four rak'ahs with one tasleem.

As for waiting for the completion of the verse (ayat), it is more befitting and closer to honoring the sacred ordinances of Allah to wait for its completion.