Can you exercise so hard that you go over your max heart rate? if so, is it dangerous?

No: Really no! you would get exhausted before too long. If you do have a heart issue, though, then it may get acutely worse during strenuous exercise and that would also make you stop.

Exercise and pulse: Young people can easily exceed the recommended pulse rate of (220-age) x 0.7. First off, it's an artificial, but fair estimate for the average person in average condition. Use it as a gauge for measuring cardiovascular fitness. As you get fit, equivalent amounts of exercise should require lesser heart rates; greater exertion can be done with similar heart rates. Don't over think it or overdo it.