Breaking suggestions up by numbers in case people want to offer different advice
1. your structure is adequate to support the weight of a metal roof as long as you don't live up north and expect to get snow piled up on it.
2. However, the weak points is that the beams are bolted to the posts and not sitting on it. Notching the post so that one of the beams is sitting on the post will add a lot of strength. The rafters will be sitting on the beams perpendicular to the house. Those are the ones that need to be sitting in notches The beams parallel to the house won't be carrying much weight at all. Leave them bolted. It would be more ideal if your pergolas was rotated 90 degrees, but not a big problem.
3. Also, the roof will catch a lot more wind than just an open pergola or with cloth that isn't rigid. Add braces to the posts like this to keep it from shifting in the wind.
4. No new central post is required. Ridge beam gets located as drawn with the short 10" posts, and then the rafters but up to it. If you build it right, the short 10" posts won't actually be carrying any load, and it will all get transferred out to the beams perpendicular to the house. Your 8x12 beam will only be there to keep the roof from pushing the posts apart and to help temporarily locate the ridge beam. No weight will be on it once the rafters are in place.
5. For your cantilever span, it is recommended to be 1/4 of the beam span or less. Use this to size your rafters so that it will be safe to walk on the roof. Table is for decks, so you can probably go smaller on the size if you want. Going a little longer on the cantilever is probably ok too since there will probably never be more than 2 people on it at a time. You can also brace it back to the post, but that won't look very good.
6. Will the rafter hit the house? Don't know. buy a 8-foot 2x6, set it up there and see if it clears. Then move it until it does.
7. Don't forget that for a low profile roof, the rafters are working very hard to collapse down and push the "walls" out. nailing them to the ridge board is probably fine up top, but they will need to be secured with some kind of bracket to the existing pergola beam to keep them from slipping out. Something like this would be ideal if you want the cathedral cieling look:
or you can add a 2x4 between the rafter bottoms to solve the issue like this (labeled as ceiling joist):
8. Construction tip: The rafters will be unstable until the roof is on. You don't want them to domino down. So make sure you don't stand or climb on them until the roof is attached and adding strength. First roof panel should be attached with you standing on a ladder, then you can work out from there.
