“3. If the badeken is see-through, doesn’t that defeat the purpose? ”
How can you ask “doesnt that defeat the purpose” if you dont know the purpose?
There are many reasons as you point out. and it is hard to list “each of them.”
According to some the badeken is the chupa I though this was tur but I cant find it now. Tosfos Yoma 13b says Kalalh wearing veil is chupa, though Iremeber a shita that it is chasan spreading clothing on her. (the reason for the yekke minhag)
Other point to imahos either Rivka who covered herself wit hcloth or LEah who yaakov didnt recongnize so she must have been wearing a veil (I guess according to this last one a see through oen would defeat the purpose, though this is a strange purpose to copy to the tee)