Foundations are tricky to respond to over the internet and their restoration can get expensive. The rock foundation just needs to be tuck pointed. Loose sandy morter should be scraped out and replaced. If the rock is deteriorating, it can be reinforced in several ways, but it is important to address the moisture problem that is causing the issue. This could be as simple as gutters and surface grading, or as complex as installing a curtain drain.
The addition on the back of the house could have contributed to degradation if it changed drainage, otherwise, it probably does not impose any load on the actual original foundation. The settling of the block foundation is caused by an inadequate footer or improperly prepared foundation excavation or both. The fix is expensive and probably requires a contractor familiar with foundations and structural repairs. The repair may need engineering and permits.
Were you planning to deal with this yourself as a DIY, or just looking for ideas?