From your answers (sorry I can't follow the math) would I be correct in concluding that:
1. The heavier rider's extra mass causes him to accelerate faster down the hill solely due to the effect of gravity in an atmosphere?
No. Gravity would cause him to accelerate at the same rate as another rider. However the gravitational force would be stronger.
2. That his assumed larger cross section (which I called girth) would slow him down due to greater air resistance?
YES.
3. That his tires have a greater contact area with the road thus increasing friction (heat) thus slowing him down?
YES, but only a miniscule, trivial amount
4. That the air resistance and friction, however, are less than his greater gravitational acceleration meaning that he would get to the bottom of the hill first?
The air resistance is less than the gravitational force, not the gravitational acceleration.
To the other part of my question... Assume there is another hill after the first, the guys are still coasting, would the lighter guy catch up on the way up the hill or come to a stop further up the hill than the heavier guy... ?
NOT if they are coasting the whole way. In a vaccuum they would coast down and roll up the same amount, but in atmosphere, since the light guy loses more of his momentum to air resistance on the way down, he won't coast uphill as far.
Hope this clarifies my question
Thank you for your time and knowledge
The difference between force and acceleration can be illustrated thus. If you hold a pound of butter in one hand and a penny in the other, you can feel that the butter has a greater gravitational
force ie. it pushes down harder on your hand. However if you drop them, their
acceleration is about the same - they both pick up speed at the same rate (until air starts to impede their acceleration). Similarily the light and heavy rider will initially accelerate at the same rate until they get fast enough that air starts to interfere with further acceleration.
Hope that helps.