These are great questions, and the guys at xkcd did a really good job answering them with not only text-based factual explanations, but also a wonderful comic-based visual explanation.
The bottom line is that staying in orbit about a planetary body (Earth!) is more about VELOCITY (i.e., speed) than it is about ALTITUDE.
Yes, there’s a minimum altitude required to get above the very draggy atmospheric effects, but there’s a difference between a sub-orbital launch (e.g., the first two Mercury program launches of Alan Shepard and Gus Grissom) or an X-15 extra-atmospheric venture and a true Earth-orbiting vehicle (e.g., Space Shuttle, ISS, etc)… and that difference is HOW FAST IT IS GOING!
That’s just a smidge over
ONE PERCENT DIFFERENCE
between being in orbit…
and “not being in orbit”.