First picture -
Never seen this layout before (but I'm only a pilot.....) but you can see the gas path leads back to the combustion chambers then does a 180 degree turn before passing through the turbines. The exhaust then exits through the fin-shaped ducts around the outside of the engine; you can see they have small vanes inside to change the direction of flow another 180 degrees.
This would be called a Reverse Flow engine, and the turbines are driving a fan at the front, which will be a major contributor to total thrust. The exhaust "stacks" around the mid-section are also contributing to the thrust, which is coming out of several outlets instead of one big one at the back. I would guess this is a medium bypass ratio turbofan.
The advantage of this may be to allow installation in the nose of an aircraft, rather than in a wing-mounted pod, with the "stacks" protruding around the nose section.
Note the P&W PT6 turboprop, in which the gas path does two 180 degree turns and two 90 degree turns on its way through, exiting via two large exhaust stacks near the front of the engine.
I'd love to know which types this powers.
The Convair 990 had engines of this layout, maybe this is one (you don't give details of the engine designations). In a more conventional turbofan, the last stage turbine drives, via a shaft to the front of the engine, the fan. In this, to avoid using the shaft (weight, lubrication, vibration, complexity considerations), the fan is simply attached directly to the last turbine stage, in a seperate concentric duct. I would guess the efficiency would suffer due to the difficulty of sealing/seperating the hot stream through the turbine from the cold duct. I would think some hot air would leak out into the cold duct due to its higher pressure.
This is an un-ducted fan. The hot section turbines drive two rings of contra-rotating blades on the outside of the engine. They were test flown on a 727-100 and an MD-83, which displayed at the Farnborough Air Show, and the type powers the Antonov 70 transport.
This type is quite efficient, makes less noise, but there is no protection in case of blade seperation, and the industry thought it too revolutionary.
So there are some basic descriptions, but I'm no engine expert. Hopefully we'll be enlightened by someone who is!
Regards - Musang