Is this mold? Is it dangerous mold?
The first photo could well be mold. Testing will confirm/deny. As to danger, the answer is, 'probably, yes, it presents a hazard to occupants'. There are lots of variables to consider, though. 

It is very common for HOAs to be responsible for roofing, but you need to contact theirs to see. A paper trail is very important in matters like this.

A mold remediation specialist can weigh in on the rebuild versus rehabilitate question, but my instinct says that you'd want to strip off and replace the affected sheathing.