I've heard a lot of advice about descending mountain roads involving cornering and braking. I want to know how to go faster when descending on the long straightaway. Is it worth pedaling at speeds above 40 mph or should I just tuck in my legs? Is there anything I can do to my posture beyond dropping down to the lower handle bars and getting as low as possible? Is there any adjustment to the bike fit that could help? Where should I put my weight on the bike? Any other general speed increasing tips?
Your question is missing specifics such as hill grade, but let's assume you are talking about steeper grades where it is relatively easy to hit speeds above 40 mph. Second you didn't mention environmental conditions (such as cross-winds) as some positions become rather dangerous if you are hit by a cross-wind or are descending a rough road.
Focusing on Body Position
While equipment has an effect, your single biggest gains will be improvements in your position on the bike. However please note that some of the more aerodynamic positions also unbalance the bike making it more unstable, increasing the probability of a crash.
A reasonably safe and efficient position is to keep your weight back and get your your body into a wedge position (see image below). By getting down far enough the wind should hit your back rather than your chest, preventing your chest from acting like an air scoop. Also notice that the hands are brought in as close as possible to reduce drag generated by the arms. You should also bring your legs in as close to the frame as possible. Your goal is to present as little profile as possible.
You can further tweak this position by bringing your body further forward and your face closer to the handle bars. This reduces the gap between your handlebars and your face/head reducing turbulence and shielding more of your lower body from the wind. In this case the rider has his hands on the drops as he is also navigating turns.
More Unstable/Dangerous Derivatives
It is possible to get into even more aerodynamic positions. The fastest position I have found is taking the position found in the first or second image and getting your head and body in front of the handle bars and tucking in all your extremities in the remaining spaces (the rider below is partly doing this). In the most extreme case your face should be an inch off your front wheel and your chest on your handle bars (not shown).
DISCLAIMER - In such an aggressive position, you cannot see properly and if you hit any sizeable bump or are caught by a cross-wind you WILL CRASH. That said it is also very fast and can be dangerously addictive. I have found I could gain an additional 10-15 km/hr over more safer positions, but only typically do it for short stretches.
Once you get to a certain speed, and it varies, it's about drag...aerodynamics and hub/rolling friction (mostly hub).
Pedaling can actually generate turbulence such that it will hurt your speed rather than help (keep in mind that turns, etc. may require some watts to be put back in, but you are asking about the straight). Putting your feet even is usually the most aerodynamic, but you should play with your position and see what "slips" the best. For me it's even with my feet level.
Body position is more about your aero profile than about your weight, that said, your rear wheel has a bit more drag due to the freewheel's pawls, so shifting your weight forward will usually gain you a small amount. I say usually because your front wheel is usually not built as strong (probably a radial) and can deform (we are talking REALLY small differences) such that you can lose shifting weight forward. Again, try shifting your weight forward and back and find the sweet spot.
The more you reduce the profile being exposed, in general, the less aero-drag you will encounter. Hands in the drops, back flat and down to the bars, possibly sliding forward or off the saddle and dropping your butt.
Playing with the position and you will find little tweaks that help you. Each person is a bit difference. You could adjust your bike for lower profile, but I would recommend against that...you won't gain much and you lose at everything but the straight descent.
Other bike things: Hubs. Others may argue, but the difference in a straight descent of all the different aero-wheels isn't really that much (straight flat is another story). What does make a big difference is fast hubs. I like Hawk Racing's wheels for this reaason, there are a lot of great hubs out there...do the spin test...the one that spins the longest with the same starting impetus will usually do you well.
Finally...descend safely. Don't get into a position that compromises your control and comfort on the bike. At speeds above 40 mph, you need to be in control of your bike. At 50 mph even more so. Your bike will act differently and the road ahead will come at you fast. Your stopping distance is greater than that of cars and motorcycle. Stay safe.