1) Hmmm, somehow I got it in my head that only the tread is re-enforced, but I see from an online search that is incorrect.
One issue that can happen with high profile tires is rebound under-damping. In the extreme case, my backhoe has 4' tall tires with a 1' sidewall. These tires are the entire suspension of the vehicle, since I do not have the optional active suspension feature. The backhoe is unstable above about 15MPH because it bounces uncontrollably. I would not expect that kind of mis-behavior from a car (the backhoe also has CG and moment of inertia issues), but when you increase the profile of the tires of a car you are adding undamped springing.
My experience is that lower profile tires give the vehicle a more "direct" feel. Keep in mind than handling and cornering performance, although strongly correlated, are not the same thing. Handling == how easy it is to navigate turns at speed. Cornering performance == how fast a turn can be navigated regardless of the effort involved.
2) I think a bicycle tire has more loading per amount of material than a car tire. My bicycle tires have to be able to handle 100lbs of loading with no suspension (i.e. shock loads are significant) and with most of the load able to shift fore-aft substantially. They weigh 1/2 pound. Giulia's tires handle 15 times the weight, but weigh 50 times as much. The bicycle tire is not fiber re-enforced rubber but instead rubber sealed fibers; they are almost all fiber-a mix of Kevlar and Aramid fibers. Bicycle tires made a huge jump in performance about 15 years ago. They are much more expensive than car tires for the amount of material you get.
3) If you needed to tune the wheels on your Triumph from time to time the wheels were clearly not designed using the principals put forth by Jobst Brandt. I believe he published the 1st edition in the early 1980s. Rumor has it that he once was an engineer at Ferrari, but I know him as an HP employee. At HP he was able to get access to the computing power needed to do finite element analysis on a spoked bicycle wheel (difficult, circa 1980) and found that "common knowledge" about how a wire wheel works was 100% wrong. The major points that I remember are:
A) The spokes must be as tight as possible to get the maximum strength from the wheel. Spoke tension only decreases when the wheel is in use. This is the single biggest problem with most older wire spoked wheels.
B) The spokes are springs, so that thicker spokes do not make a stronger wheel.
C) The spokes should be straight except for an elbow at one end. The elbow should be thicker than the rest of the spoke.
D) The spokes must not be allowed to rotate while the nipples are turned or they will appear to loosen in use as they "untwist". The nipple threads should be slathered in anti-seize or it will not be possible to achieve A) or D). A special hardening anti-seize compound is best.
E) The spokes should be overtightened and then relaxed slightly. Brandt's method for doing this without breaking anything when building a bicycle wheel would not work for a car wheel.
A spoked steel and aluminum bicycle wheel is about 2/3rds of the weight of a full carbon fiber bicycle wheel of similar strength. Although the front wheel of a bicycle has the rim centered over the hub, the rear wheel has a substantial offset in order to make room for the gears on the hub.
Building a wire wheel properly is labor intensive, so maybe they got too expensive? Racers migrated away from them in the late 1950s, long before information about how to design and build them properly became available.
4) I can't tell from the picture. The wheel looks like it is installed "inside out" in the picture.
My Etype had inboard rear brakes. Changing the pads was not difficult. Changing the rotors involved tearing the whole back of the car apart. Heaven help you if the seals in the differential start leaking (as purchased, I could see daylight around the differential seals, plus the calipers were badly rusted inside-what a mess!). The Etype has removable panels in the trunk to ease access to the rear pads, but I found I could get at the pads from underneath reasonably easily. Etype rear brakes are notorious for overheating on the track; Jag even produced a track kit for reducing the problem.
Both wheels and tires have pressure and load ratings. On my pickup the wheels are rated 95psi max and 3500 pounds max, while the tires are rated 115psi max and 4650 pounds max. One has to use the lower figure. Axle ratings also need to be considered.
For bicycle tires, wider lowers the rolling resistance as does higher pressure. However, wider generally means a lower maximum pressure and wide high pressure tires ride very rough making it not as straightforward to choose as it sounds. It is unclear what works to minimize rolling resistance for car tires.
Yes, car, bicycle and motorcycle tires have improved a lot in recent times. In comparison medium and heavy duty truck tires have gotten cheaper but not much better.