1- It is permissible. If one’s intentions are 100% pure, then it is not even makruh.
2- No it is not wajeb as long as the intentions are pure.
3- If the videos are professional, appropriate and purposeful, and don’t comprise hijab in any way, it’s permissible.
4- Saying that to her could be haram.
5- If it’s strictly professional it is ok
6- It is not haram to talk to them about Islam