ijuin

Sure there's a limit, but there's some distance in between "normal operating power" and "about to burn out", where the extra power is putting strain on the engines, but it is expected to take minutes/hours/days before it actually breaks. See War Emergency Power for a real life example--the P-51 Mustang's engine could be over-driven for short periods to get up to 60% above its rated power level, but five hours at this level was enough to require a full rebuild of the engine, and even five minutes of it was enough to require a full visual inspection of the engine's internals for damage.

If by "robots", you mean sapient ones like Data, it's pretty well established that Dr. Soong made breakthroughs that nobody has yet been able to duplicate, with Data's creation of Lal being the closest to success that anybody has gotten. In the episode, "The Measure of a Man", Cmdr. Maddox had wanted to reverse-engineer Data in order to attempt to duplicate him, and the plot of the episode revolved around establishing that Data had the right to refuse to be taken apart. Other sapient Artificial Intelligences have also mostly been stumbled upon "by accident", such as the holographic Moriarty or Voyager's Emergency Medical Hologram Mk. I. It seems that Federation technology is not yet up to the challenge of reliably creating sapient AI on demand. If, however, you mean non-sapient automated drones, we have seen those being used, especially in areas hazardous to organic life--e.g. exterior work on starships in space dock, or the Exocomps. Actually, an ion rocket is a good example here. Any engine that accelerates its reaction mass using an electromagnetic field will accelerate it more strongly in proportion to the strength of the field. In other words, increasing the power to the electromagnets will increase the specific impulse of the engine. This, in fact, is how the VAriable Specific Impulse Magnetoplasma Rocket (VASIMR) engine achieves the "variable specific impulse" in its name. Of course you're a Looney--it's even in your name!

An engine’s “rated” power output is not the maximum that it is capable of—it is the maximum “safe” output. Whereas civilian engines are designed to be unable to exceed their rated output as a safety measure, military engines in real life have no such limits—they can be over-driven, though at the risk of excessive strain causing a breakdown. It is analogous to afterburners on a turbojet engine—A lot of extra energy/fuel is thrown into the engine in order to get extra thrust, but at far lower efficiency than normal operation, granting diminishing returns. In Star Trek, we see the warp engines being over-driven in this manner whenever they go to “emergency” speed, above the rated warp 5.0 (NX-01), 8.0 (NCC-1701), 9.2 (NCC-1701-D), etc.

I think that we need to distinguish between powerplants and engines here. The warp reactor ("warp core") provides power for the warp engines (those huge nacelles), which are the most power-hungry system on most ships. The impulse reactors are a set of fusion reactors that provide power for the impulse engines (those red glowy things seen on the aft side of the ship), and also provide secondary power to the rest of the ship when the warp core is offline. Now, the key thing here is that one type of reactor can be used to provide power to the other type of engine if need be. For example, in "Star Trek Beyond" (the third JJ movie), when the Enterprise loses her warp nacelles, Scotty rerouted the warp core's power output to the impulse engines. Likewise, if the warp core is offline (or destroyed), power from the impulse reactors could be diverted to the warp engines--though this would result in them being seriously under-powered and would give a much lower warp factor, e.g. Warp 3 instead of the normal Warp 8 or higher. So, warp travel at relatively low speed is still possible without the warp core, as long as the warp nacelles themselves are still functional.

Sounds like my cat—when he sees a moth or a fly he will chase it.

Furthermore, Federation starships are not held together by the strength of their physical structure--they are held together by forcefields--the "structural integrity fields". The structure only needs to hold on its own under relatively low strain because when the ship has power, the forcefields provide 99% of the strength. As for the shapes of ships, apparently streamlining is meaningful for warp travel--keeping your frontal area reduced, for example, would reduce "how much" space you need to contract in front of the ship, and therefore the amount of energy required. The more-streamlined shapes probably allow for greater energy efficiency.

Yeah that's why I said short, like maybe 30 strips.

The magic tag/duel thing sounds like it might make a fun short NP story.

The Enterprise-D overall is a bit over six hundred meters (two thousand feet) long. The secondary hull (i.e. the non-saucer part) is three hundred and a bit not counting the warp nacelles. The hard part of getting people out of there is climbing the decks--the lowest deck is Deck Forty-Two, and the interface between the primary and secondary hulls is somewhere around Deck Twelve or so, which means up to thirty decks to ascend, with the elevators probably not having enough capacity to carry everyone quickly. To evacuate everyone that quickly, they would have to use the transporters to pull out those who were too far away. With a stated eight transporter rooms in the Saucer section, and assuming six people per transport cycle and two transport cycles per minute over four minutes, that allows evacuating about 380 people via transporter in four minutes, which is a third of the Enterprise-D's entire crew. As for crashing with the top up, what little control they had during descent was being used by Data to put them into the safest orientation for the landing. Standard complement for the Enterprise-D was between 1000 and 1100 crew, not counting passengers and children. Deanna Troi was officially a Lieutenant Commander at this point in the story--there was an episode during the series where she was taking the Command Officer's examination, where she had to send Geordi La Forge to his "certain death" in a simulation in order to prove that she was psychologically capable of sacrificing a friend in order to save the ship if need be. However, yes, you are correct that it should not have been her, but rather Data, at the helm for the entire sequence.

My point was, gold at present is at a significantly higher price relative to most goods and cheap services than it was in the days when the value of currency was pegged to the price of gold, and this is because there is less gold available in comparison to the overall amount of goods and services. If we had maintained the backing of currency by gold (i.e. had not abandoned the Breton-Woods system of convertibility of currency to gold at rates fixed by governments), then there would necessarily have been massive deflation over the past several decades.

Here is the scene, if you wish to watch it:

The engineering section blew up when its warp core destabilized after the Duras sisters’ ship put a torpedo through it. The surviving (damaged) saucer section was then forced to make an emergency landing on the planet below.

And that $10 grand was out of a total budget per episode of about $100 grand. Yes, that’s right—every single transporter sequence took up about a tenth of the episode’s entire budget.

Basing your money on a commodity (such as a metal) always brings the problem that you can not consistently grow your money supply to match your economy. If the economy grows more than the money supply, then you get deflation, which is economically equivalent to everybody receiving interest on all held money--i.e. it encourages people to hoard money and not invest it in creating/adding value. Let's compare some prices: In 1908, the US dollar was worth 1/20 of a troy ounce of gold ($20/oz.). The Ford Model T debuted that year at a price of $850, equivalent to about $24,000 today. That puts the price of the car at about 42 ounces of gold--3 1/2 troy pounds. Today (03 June 2020), the price of Gold on the New York commodity exchange closed at $1,700.80/oz. 42 ounces at that price would be worth $71,400. Thus, the value of gold has increased by a factor of three relative to general price levels over the past 112 years. Let's say that you want to grow your economy at 2.0% per year (an slightly-below-average amount for industrial nations over the past three centuries). In order for gold-backed currency to keep up, you would have to mine as much gold over the next forty years as the entire history of mankind. And then you would have to double that amount over the NEXT forty years after that, and so on. Eventually you will need more gold than could be recovered even if you diverted all non-essential activity towards gold extraction.

Yes, well, Luna did attempt to bring about an eternal night, in which all life would freeze to death from the lack of sunshine. Allowing her to continue it was not really a valid option. TOS sets and props looked like cheap cardboard because they were, because the network gave them peanuts for a budget even by the standards of science fiction shows of the time. Roddenberry had wanted for the Klingons to have the forehead ridges and such, but couldn't afford all the makeup technicians and equipment that would have required.