You are a sincere and intelligent sister, and I appreciate your commitment to sources. Yet, I have the following comments:

The source you cite from is, unless I am mistaken, the commentary included in a recent Saudi translation of the Qur'an which they claim is "agreed upon by ibn Kathir,al-Qurtubi, and al-Tabari." It is not itself the tafsir of ibn Kathir, al-Qurtubi, or al-Tabari. If you gave some strong evidence directly from these sources, then I would consider it.

Also, my main question - whether the purpose of hijab is to "protect women from the lustful gaze of men" is not shown in the Quranic aya or hadeeth contained in this long section of material. At least I do not find it. Please, can you can indicate the specific verse or hadeeth in what you posted which shows that this is the purpose of hijab?

I will leave off the other issues for now.