You are right. Most people apparently don't push hard enough when performing their first CPR, I guess that's what our instructor meant when he said that broken ribs (as a result of CPR by non-professionals) are usually caused when pressure is not applied to the sternum from the top. Nonetheless, he continued to underline the importance of a timely help, no matter how small, even if not performed perfectly or professionally.
The instructor also touched all of the other points you raised (including the first round of CPR). For the better part of the day he covered what to do when no AED is available and you are on your own with a patient. I really liked this class. None of us is a pro after a day-long course, but it really conveyed the message that even us lay people can make a difference until the trained professionals arrive.