Is performing four rak'ahs of Qiyam al-Layl before sleep, with taslim after every two rak'ahs, then performing three rak'ahs of Witr with a single sitting and a final tashahhud before Fajr, followed by two rak'ahs of Tahajjud, considered seven rak'ahs of Witr, or four rak'ahs of Qiyam and three rak'ahs of Witr?

Your prayer is valid and sufficient, and it is part of Qiyam al-Layl (night prayer). It is preferable to conclude your night prayer with Witr, as this was the practice of the Prophet, peace be upon him, and his saying: "Make the last of your prayers at night Witr." Praying two rak'ahs after Witr is permissible to show permissibility, but the Prophet, peace be upon him, did not consistently do them. The more appropriate and better course of action is not to perform them, to avoid disagreement. Your performing Witr with three rak'ahs without a tashahhud in between them is permissible. The four rak'ahs you pray at the beginning of the night are definitely from Qiyam al-Layl, and they can be considered Witr according to some opinions, as Witr is part of Qiyam al-Layl.