Can you still get into a good university for medical if you are not in Honors sciences in high school?

Answer 1

You want a bachelors, not an associates degree.

If you're talking about a university for your bachelors degree, you can still get into medical school from whatever 4 year college you end up at. If you didn't have honors sciences, you might not end up at the most prestigious school (or may not get into a science major), but neither is a requirement to get into med school.

Once in college, very little of what you did in high school counts anymore. It becomes about what you do in college.

Answer 2

Yes. However, you may be required to maintain a certain GPA in your AA requirements to proceed to your major. Another good way to do this is by getting a transfer degree from a community college and bringing your grades up in those science courses. You will want to get your AS (Associates of Sciences) rather than your AA if you go that route.
Good luck.