Hello GTG and welcome aboard!
Wow, I have to be honest I would most definitely tell you to tear the thing down & just build a new garage, salvage what lumber you can by all means if you want to, but the walls being framed on 3' centers is scary and definitely not up to any sort of code even if they're 2"x6", and I'd bet they're just 2"x4".
It could be that if you tear down the garage you can't rebuild due to setbacks or other codes. Sometimes you must preserve one wall in order to rebuild. So first thing that's in order is a visit tothe local building inspector's office, you'll find that's things will go alot smoother and there are no surprises if you do things the right way.
The part of your post about the scabbed lumber on the joists, is most of this at the lower end of the joists? If that's the case I'd say this was done during some previous renovation when either the roof or soffits and fascia was redone.
One other suggestion, make a material list for a complete new garage and get an estimate on it, then compare it to the estimate for materials to rebuild what you have. Then compare the two. But like I say if you live in a city or town, there's probably codes to follow & permits to pull.
Hope that helps a bit.