How much resistance comes from each part of a bicycle? How does one decide which part of a bicycle is the best candidate to upgrade or tune if the goal is higher speed for the same energy? For example, should one upgrade wheels, or tyres, or change to lighter parts, or to reduce aerodynamic drag with fairings? 

Is there any way to compare the influence of each part? How much power can you save, and is it significant enough that you can recognize the difference? For example, do aero improvements make sense if speeds are very low and, if not, how can you determine the speed above which it does make sense?

We are reinventing wheel here.
Aero formulas from Sheldon Brown and racing bike chart


Few similar links answering this question:
- resistance types

- aerodynamics part 1

- aero (exploratorium.edu)

- human body front area depending on pose in case it will be possible to ride in horizontal position drag must be way smaller as front area will be at least 5x smaller.
Answer: This question cannot be answered in a simple tabular format because the resistance of every part depends on every other part.

IE, a wheel and tyre and spokes will have an effective "cross section" which is the hole it has to punch through the air.

That area is mitigated by the shape's curves.  From wikipedia: 


So for simple shapes in isolation, the drag coefficient is known, and you can measure the cross sectional area in square metres.

Your problem is that a bicycle is not a sphere or anything simple - its a complex series of parts and they're hitting the air at different delays.  So when the air hits your downtube, its already been distrupted by the front wheel, forks, and headtube, as well as being in close proximity to your shin which is a periodic displacement of air.

To approach what you're asking - you'll need either to buy time in a wind tunnel, or fit a power meter on your bike and measure your times.

Doing this with scientific rigour means


doing each run at least 3 times
riding to a set power that you personally can maintain for the whole distance - no more and no less.
riding a distance of at least 30 minutes
having a route with no chance of stopping at traffic lights or similar
in an environment with consistent winds/temperatures/humidity across all your trials
and having a way of measuring your time as accurately as possible between a well defined start and stop point.


Then swap the one part you're testing for the other part, and repeat the three runs.

The difference in time will show you how much power you've saved/lost with the one variance.    If you want to test 5 types of pedals, that's 15 runs.

A circular route will help too, if you can find one that works for all the above requirements.

Ideally your rider would not know which parts are being tested on each run, so they can not be swayed to push harder or softer subconsciously.

One might reasonably assume that Manufacturers would release this kind of data, especially for their high-end items.   And they do with statements like "saves 17 seconds in a 40 km time trial, over last year's model."  Which is relatively useless as a comparison.

tl:dr - there's too much interdependence to make a simple table that is also accurate.