Yes, there are already umpteen answers to this question. However, I will attempt to answer it in a way that none have yet done.
You say that your merfolk are at “WWII era warfare” — I take that to mean that they are at the second part of the Great War, and therefore are a parody of our own history, or some version of it.
Therefore, I shall suppose that the human nations and empires of that era were moved over to the eastern ocean: the Americas are in the Atlantic, Africa is in the south of India, Europe is off the coast of Japan and China — with the Isles conveniently separated from the main ocean by the ‘Nippon Insurmountain’?
Obviously it isn't a perfect conversion, because freshwater lakes do not have properties which equate them to islands for us, and I base my answer on the premise that these merfolk require salty water.
I'll say that they cannot control a heterostatic pressure of their bodily cells, and so are unable to venture from their home depth — which is what?
Are these merfolk bathic, occupying the deepest depths and possibly surviving off the sulfurous hot vents issuing forth from the cracks in the trenches?
Are they less extreme, and living at the transition from lit oceans to the dark depths? Feeding from the detrius which rains down from above, like mana from the heavens?
Or, are they shallow folk, farming the phytoplankton for nutrients?
Whatever the case may be, they are limited to it, and so it merely serves to provide them with larger expanses if they can occupy the seas above continental shelves.
Now, being as they are a parodical version of our history, you ask for a description of their Überlandkarts (U-boat, Unterseeboot).
Well, keep in mind that these people have probably already discovered a way to travel under, over, or through the massive obstacles of land. Why? Because these merfolk like to expand their limits. If nobody else has done it yet, then to do so is to reduce the competition and to allow previously stifled people a chance to thrive.
If they were shallow, it is quite simple. They've already begun colonizing the land with big umbilici which they've built against the rivers flowing into their oceans — remember that I suppose they require salty water. The same technology can be used to build bubbles on the land: waystations off the roads, where planktons can be cultivated.
Ah, yes, their technology. I will say that these people have technology which is much nearer their own biomechanical systems than anything else. Okay, so they aren't exactly like people, naked mediocre and extracting their living from the unwilling earth about them.
The deeper merfolk would be the ones who would require vessels to travel out of their stratum. I don't think digging would be an optimal method of expansion — though it certainly wouldn't be unattempted, especially with the folk huddling around the hot vents. Those ones are the most promising, so I'll go with them.
The hot vents, or hydrothermal vents (see to Wikipedia, NOAA, or PMEL), which exist on the ocean floor exude water heated to temperatures anywhere about the range of roughly 300 to 400°F, saturated with minerals, and with a basic pH. From my recent reading, many of the characteristic mineral chimneys which occur at these focused vents are mostly made of a copper–iron sulfide e.g. chalcopyrite on the insides — and zinc sulfides on the outside of the porous chimney walls.
Now, whether the merpeople are able to smelt any of the abundant ore or not relies on whether they are able to employ a means by which to separate the ionic metals from their companions to produce elementally pure metallic compounds.
There are two major ways by which to extract metal from ore. The first is chemical: chemically, whereby you introduce an ionic compound which causes the undesired components of the molten ore to either float or precipitate away, leaving the metallic elements alone; electrically or galvanically, whereby you use electric voltage to perform the separation, attracting the metal to the cathodes of your galvanic cell.
Well, anyways.
These merfolk, establishing their cities around the hot vents, would eventually learn that they could gather minerals from the distant brine pools. The brine is laden with alkali halide minerals, e.g. sodium chloride, bring them to the vents, and create voltaic batteries by separating the copper and zinc ions by their specific elemental gravities.
I've not worked out whether this is entirely possible, mind, but depending on the rigor of your world's scientific consistency, you may be able to simply say that it happens.
Suffice it to say that these merfolk would've already been building metalcraft in great smithies constructed over artificial extensions to the hydrothermal vents.
They would build vessels contain their own native pressures and allow them to venture upwards out of their depths, discovering the vast anti-depths above them. I figure that they would take comfort in the presence of a floor, much as we do, and so would eventually learn that it climbs upward.
They'd be establishing colonies all along the continental shelves — this is during the ages of 1600..1900.
Here, I must raise issue with the plausibility of them developing Überlandkarts, or even Überseeboots, which would venture to the surface of the oceans.
See, most of our submarine vessels didn't venture far from the ocean surface. The differences of pressure which they were built to withstand at even 1500 feet were in the ballpark of 660 psi absolute:
$$P_a = \rho h + 14.7\frac{\text{lb}}{\text{in}^2}$$
A very simplified version of the equation for the relationship between absolute pressure ($P_a$) in a liquid of a certain density ($\rho$) at a depth ($h$), and is valid for static pressures in a range of depths below Mean Sea Level where the water has negligible change occuring with its density.
Most of our submarines don't go so deep. Going to the benthic depths was not a routine activity during 1940.
Nowadays, we do built vessels capable of holding pressures in excess of 3000 psi, but those are built much differently than a submarine. Submarines have much more complex shapes and many more necessary seals to prevent leakage and to withstand buckling where the shape deviates from a perfect sphere.
Enclosing greater pressures on the inside is easier than keeping them out, yes, but there is yet a large differential between the pressure at 30,000 feet below Mean Sea Level and at MSL.
I don't expect that these merfolk would be straying on the land any time soon. You know why so few specimens of deep see creatures are adequately studied by us? Because they deteriorate when brought up to our comparatively low–pressure atmosphere, and must be kept in hyperbaric chambers to maintain their integrity.
supmarine
since sub/sup are opposites in familiar context. $\endgroup$