Hello. I can help.
Do you have any pictures you can post for me to see? You can attach them here with the paper clip icon.
I can see the original post, but there are no images attached
Wow. That's a very poorly framed roof. The structure is very light
Yes, you can run joists perpendicular to the door. You will need to ensure that the header can take the additional load if they impose any new loads on the garage door header
If you sketch out all of the framing with dimensions I will look at it