I think everyone got the bits and pieces right. So restating some of what was said and adding a little more:
The 2x6x20's are your rafter ties keeping your walls from pushing out. In the old days they were placed every 4'. They can be as little as 2x4 for their purpose, but were usually bumped up to 2x6 over long distances to prevent sagging from its own weight, not to allow storage. If you think they will just hold some Xmas stuff and junk, undersized wood and nails are very accomodating. Heck, I have rims, body panels, iron heads and **** on trusses and I even know better. But it's a risk you take with storage creep over time.
The old diagonal 2x4 tying in the corner top plates of your garage was just temporary to keep the walls square until the roof went on. The 2x6 up to the ridge you speak of but doesn't show in the pics, those were probably also temporary to hold up the ridge board until all the rafters were in place (looks like a hip roof). Neither of these are needed now, but keep the 2x6 braces as your ridge and hip rafters are probably not sized as beams.
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If you want to solidify this existing roof and provide real attic storage:
- Remove all the ceiling-level framing. The new lateral bracing between these rafter ties has done nothing but added more dead weight to what the 2x6x20's already has to contend with. Running a bunch of purlins up to the rafters might keep them from sagging, but it actually reduces your existing roof rafter capabilities.
- Install 2x10x20'@12"o.c. ceiling joists (existing rafters look 24"o.c.)
- Install 2x4 kickers from each rafter on the perpendicular 24' long hip roof, down to the 2x10 ceiling joists.
If you want to add real attic storage by keeping the old 2x6x20's:
- Remove all the new lateral bracing, everything except the old 2x6x20'@48"o.c.
- Add new 2x6x20's in between to make the spacing 24"o.c.
- Add a perpendicular 24' long steel W-flange beam under the midpoint of the 2x6x20's. It has to be under because with the hip roof over the garage door it would clip a flush beam if resting on the top plate. Then it has to be steel because you only have about 8" above the garage door header. Then you need to verfiy the existing garage door header can take the weight, and provide a post on the opposite side in the house wall and then verify that foundation is adequate too. Then offset your garage door opener. See where I'm going?