Electric will never replace long haul jets barring a revolutionary breakthrough in battery technology. But that's not the point. Much of commercial aviation takes place on distances of around 100 to 500 miles. That is, too far to drive but not quite far enough to take advantage of the efficiency of jet engines at high speed, high altitude cruise. For those applications electric propellor and ducted fan aircraft will be absolutely game changing. It will make these flights cheaper and safer by a factor of 10 at least. The vast majority of cost in a flight is maintenance of the engine. That all goes away with electric power. It will make commuter flights an affordable daily reality for normal people.
Currently increasing fan sizes are getting problematic. That is the problem with the 737 MAX. The fan diameter of the new engines is too large to fit between the bottom of the wing and the ground. So it had to be mounted forward and up which fucked up the aerodynamics.
Two other advantages are, potentially maintaining thrust in an engine out situation. When you lose an engine not only do you lose half your power but the thrust is unbalanced. And faster throttle response. Turbine lag is a big issue with jetliners.
Note: The reasoning behind high bypass turbofans is thrust is proportional to delta v times the mass flow rate. Where power input is proportional to delta v squared. Bigger the fan the more efficient you are and the less fuel you use.
Diesel is kinda interesting. Manufactures are developing diesel engines for light aviation. I suppose you could have a hybrid diesel/electric aircraft.
I know people call Jet-powered aircraft "jets" but, that's really an abbreviation.
I think what you're asking though, is whether there are any electric propulsion systems with the same characteristics as jets - i.e. more thrust relative to speed. AFAIK, there are not, because a characteristic of chemical fuels is that increased compression and airflow can increase the efficiency of the reaction. Electric motors have a (relatively) fixed efficiency due to the battery.
The propulsion of a 'jet engine' is normally through a gas turbine, which is a type of internal combustion engine, so you wouldn't get an electric gas turbine.
Replacing the gas turbine with an electric motor would in this case produce an electric jet engine.
No, it's not. A propellor creates thrust by slicing the air and creating lift just like a wing, but in a forward direction. A jet engine's fan blades create no thrust in themselves. They provide the compression needed for combustion to occur within the engine, and thrust is created by the expelling of hot exhaust gasses.
This is done to trade the high speed of the jet exhaust for a larger amount of air moving more slowly. Making the speed of the jet plume closer to the true airspeed of the aircraft makes it more efficient.
Looking at design of turbines, a lot of air is needed above the amount for combustion to help keep the post combustion chamber turbine from melting (or just weakening to the point of failure). Some of this will be the unburnt (nitrogen, etc) components of the ingested air but a lot of design goes into moving air around components to move heat away from them.
The less air needs to be compressed for the engine then the more efficiently it will run. This is often achieved by designing one that can run hotter. This is also one of the other ideas behind having the bypass on a turbofan, reducing the amount of air that is compressed.