If I was in a circular 10km orbit (theoretical) around Earth, what will occur earlier? Will I burn up in atmosphere or be stopped by atmospheric drag?
If you're really asking about moving at orbital speed while at 10km altitude above the Earth's surface, you'll do both at the same time.
You will plow into the air in front of you, compressing it and slowing you down; the compression of the air will create extreme heat and you'll burst into flames. Since you have a great deal of speed to shed, you'll be pretty well incinerated before you come to a stop.
Much depends on your heatshield - if it is strong enough, you might survive until you have slowed down enough to that further heating is no longer a question. If it is not - you will burn... Besides - you will never be stopped completely by atmospheric drag as it is a function of your speed - the slower you get, the less it decelarates you - to the point where gravity and drag are equal - called terminal velocity.