Hi MarikaZoll,
On number 2 above, With your photos going through two steps to show up enlarged, the first image on your home page has a link url of the Post URL rather than the File URL.
When you add your image gallery, Add Image>Gallery> Gallery Settings at bottom, I believe you need to have “Link thumbnails to” with “Image File” checked. I am guessing you inserted that gallery with Attachement Page. Try to update that setting for your gallery, or re-insert if you need to.
Not sure I follow number 3.
On number 4, #FFFFFF is white, not black. Black is #000000. What I see is a white border around the image on the second click with the lightbox, and then a black background. Looks good to me, not sure though what you want.
number 1 above, could not figure what you mean. I watched both videos and say no issue with it. Maybe it is a browser specific issue. What browser are you using or did you fix it.
yunus