- Does the age of the aircraft increase the aircraft's maintenance expenses, fuel consumption, and electrical shorts?
- If so, by how much?
- And is this a reason why planes get scrapped?
The very simple answer to your first question is just yes.
As something (or someone) age, more maintenance is required. It varies from case to case and you cannot have one size fits all rule or guideline.
Getting to your last question, it also depends on an individual case. Please also note that when an airplane is grounded, it is not required to be scrapped in all cases. Sometimes museums are interested in it, or it can be installed as a roadside monument or placed in an aircraft boneyard.
Regarding when an aircraft needs to be retired or scraped, these two articles are a good read:
Farhan poses some great points and offers some great articles but for the sake of the other side of the answer I will offer up some other points mainly related to GA.
While the general answer is yes, I will offer an answer that "Hours are more important than years".
From a pure engineering standpoint wear and tear is more a function of cycles than time. An new aircraft that is used as say a trainer and sees lots of hours a year may be in worse shape than a privately owned rarely flown aircraft from 30 years ago. To you points,
fuel consumption (and oil consumption for that matter)
Both more a function of the engine than the airframe. Engines are overhauled in and around 2000 hours for GA planes (or if there is an incident or problem). A freshly overhauled engine will (or at least should) preform like a brand new engine and should burn oil and fuel as such. Depending on how often you fly there are plenty of very old planes out there with low hour overhauled engines that run like a top.
In general yes older planes will cost more to keep up as they may see more broken parts due to use. On the other hand older planes tend to be simpler and parts are often cheaper. One could argue its cheaper to upkeep an older Piper Arrow than a brand new Cirrus (granted these are very different planes). But the Cirrus sees a very pricy annual as a result of its ballistic chute and I'm sure the carbon fiber is not cheap to fix if something goes wrong.
There is another point to note and this very much depends on the plane but lets break GA aircraft into 2 categories. All metal (or composite) and fabric/wood planes. It should be obvious that fabric covered planes are not as durable as their metal counterparts and can be harder to leave outside in weather which means you will need a hangar. Wood planes or planes with wood components (early Mooney's) suffer from rot and cracked wood. Then again metal planes can suffer from rust and corrosion. You may also be hard pressed to find a mechanic who knows the ins and outs of a wood plane these days.
The sweet spot seems to be the early but not first all metal planes (think Piper Cherokee). These planes are simple and easy to fix, contain parts that are still made in many cases making them cheap to own. You can buy a beat up 140 for the price of a composite 3 blade prop for some of these new planes. Granted you won't go nearly as fast, you will still fly and you will still own a plane.
Short answer; yes.
As with any complex mechanical system, there are several overlapping service lives of various subsystems. Simply put, the longer a machine is in operation, the more wear and tear is put on parts of the machine that aren't designed to wear out and be replaced as part of normal maintenance (like brake pads, belts, hoses, etc). You replace your car's tires every 30k-60k miles, but the drivers' side door isn't something you just plan to replace after X miles. Nevertheless, replacing or refurbishing the driver's side door after 20 years will probably give you a noticeable improvement with regards to all the things that door contains, from the hinges it opens on to the gasket that seals it against rain and noise, to all the switches, motors and servos controlling the window, lock, mirror, etc.
The same is true for an airplane; the longer the airframe is in service, the more things that aren't designed to wear out do so anyway. The difference is that with a car, if a wheel falls off or the radiator hose blows out, you just limp to the side of the road and call a tow truck. Failures on an aircraft are not so easily handled, and remember the mantra; taking off is optional, landing is mandatory. By the same token, while car maintenance is frequently stretched far more than is prudent, because the gamble is against an inconvenience of a few hours and the tow truck fee, maintenance on an aircraft is a no-nonsense business because the gamble of not doing it is the lives of a hundred-plus people aboard when something goes wrong; inspections with accompanying repairs, replacements and retrofits happen at set intervals of flight hours or press/depress cycles, like clockwork, without fail, or the plane doesn't fly.
That means the longer the airframe is in service, the more things start to reach the point where they must be replaced, either because they've worn out or are obsolete. Eventually, between the cost of replacement and the lost revenue of the plane being out of service to fix the ever-increasing number of failing components, it's no longer good business to continue operating that particular airframe, at which point it's sold, either in flyable condition to a discount airline, or for parts/scrap at a boneyard.
In addition, newer planes have a lot of advantages simply because they were developed using better technology. Engines, for instance, are a component of a plane that is not easily upgraded to an entirely new design, because of considerations like overall aerodynamics and under-wing clearance. While some upgrades are possible (the 737-100 had a much smaller, less efficient engine than modern 700s and 800s), they're expensive to apply especially to a fleet of hundreds of planes, and they often involve tradeoffs like reducing cargo area or increasing pilot workload due to less integration capability of the new system with existing avionics. As a result, turnover of an airline's fleet is a virtual necessity to continually improve the fleet's performance as well as avoid end-of-life mechanical problems.