That is, indeed, a less frequent use of the term, requiring the modifier.
No it isn't. It's your definition: distribute limited resources to efficiently fulfill needs. Distributing a unit of medication to fulfill a 100.01$ need rather than a 100$ need is more efficient, since using the same limited resources you've fulfilled a greater need. Think of it as an optimization problem, which requires a way to measure how much "need" is fulfilled.
That's one fat model gaze right there. It seems to be reliant really more on the concept of conserving the status quo, as by definition what is sought is no net negative change for any player:
Reminds me of
a comic - though not exactly Pareto-efficiency it's related (replace "happiest" with "richest") and the solution at each step is indeed Pareto-efficient.
However, in practice and as noted earlier, one may indeed shape the field of play in order to avoid such outcomes, even while generally having a market economy.
No you can't, a market economy is designed to produce that outcome by defining "need" as "how much money you're willing to throw at it". You can choose to distribute resources other than through a market, like you say for medication, but the resources distributed through the market will keep having this property.
Take for examples jackets, Alice has an extra jacket, Bob is homeless and really needs a jacket but only has 5$ for it, and rich Charlie has an entire closet full of jackets and is willing to pay 100$ for another jacket. Then the market solution is Alice selling the jacket to Charlie for 5.01$ and Bob remaining on the streets without a jacket but with 5$ in his hands. The limited resource, the jacket, was distributed to fulfill a 5.01$ need rather than a 5$ need - which is more efficient in the model's own terms.
You may believe that medication is more important than jackets and may decide to keep jackets under market distribution, but that's another question than that you could avoid such outcomes under a market economy.
The downside to simply fixing the market is that the choice of winners and losers in general falls into fewer hands, and leaves other hands with no choice. Centralized planning relies on a form of foresight and prescience that can best be achieved precisely by placing very many bets, not fewer.
This is a false dichotomy, between "market economy" and "central planning". But even so, centralized planning does not require more foresight and prescience than the current market system. Corporations are internally command economies after all.