1) That's not a "jet engine". It's a turboshaft. A turboshaft is a gas turbine producing its power mechanically at the shaft. A turbojet is a gas turbine producing its power in the form of reaction thrust out the tailpipe.
2) Gas turbines scaled down to small size (let alone "micro" size) generally have dismal thermal efficiency. All the most efficient gas turbines are gigantic (tens of thousands of hp).
I've never heard that jet engines are less efficient. From what I remember piston engines are 33% thermally efficient, diesels 36% and turbine engines are upwards of 60%+. Of course there are many types of jet engines and ways to get power off of them.
You heard wrong. Diesels under optimum conditions can easily exceed 45%, and state of the art is right around 50%. Gasoline engines can reach 40% or better (again, under optimum conditions). Turboshafts are generally around 35-40% efficiency at best-economy conditions, and dismal under low-load conditions. The very largest turboshafts can reach 40-45%, but come nowhere near to diesel efficiency at low load.
In all cases, you can increase efficiency somewhat by going to the complication of compound cycle, where you harness some of the wasted heat in the exhaust by making steam.
Large, high bypass turbofan jet engines are very efficient from an overall propulsive efficiency standpoint, but you aren't measuring the same thing (shaft power times time, divided by energy consumption).
Gas turbines operate efficiently at constant output, which a hybrid-drive system with storage can manage. They only need to kick out enough power, on average, to keep the storage system fully charged. Batteries and eletric motors can handle both high-demand accelleration, and regenerative braking. Since the turbines are running at a very constant range, and can be rated to average out power load inclusive of idle times, they can be designed for optimum efficiency within that range. Or that's the theory.
There've been other gas-turbine automobiles, including some prototypes built in the 1960s. A friend of mine test drove one, claimed it could lay a patch (spin the tires) at highway speeds. Though my understanding is that in direct-drive applications (such as that), turbine lag is an issue.
The exhaust also runs quite hot, and turbines typically emit a lot of NOx (nitrous oxides), what you get when you run atmospheric nitrogen through a high-temperature field.
It sounded like a gigantic loud vacuum cleaner even just idling, and gave the impression of straining mightily to achieve even mild acceleration. Fuel consumption was TERRIBLE.
1: https://en.wikipedia.org/wiki/Jaguar_C-X75