I 'think' that failure is when you cannot complete that rep. For instance, you do a push-up and cannot fully extend your arms and end up bringing in your knees or collapsing on your arms. That would be failure. Pull-ups are tricky since for many of us, myself included, we are not doing pull-ups but some sort of 'resistance on the way down'. I think 'failure' there should be judged by the quality... in my scenario, it is when I jump up and instead of slowly coming down in 2 seconds, I just drop.
You level up once you have completed the entire exercise on D3 in 5 minutes, including rests. Remember, until you finish the reps for that exercise, you do not move to the next exercise, taking breaks when necessary to stay 'under failure'.