German airships did not use the mooring mast concept until after the Great War; mooring masts were a British and American idea. Preferred Zeppelin practice was to keep airships in the hangar as much as possible, to walk them out of the hangar with an army of ground handling men, and they went so far as to make rotating hangars to turn them to face the wind during the delicate removal from or placement into the hangar operations.
The mooring mast idea was something British and American developers actually thought would save time, as well as avoid the need to move an airship into or out of a hangar when the winds were not conveniently in line with the hangar doors. They thought you could just park the airship moored by the nose and it would just wind-sock into suitable line. But the high mast idea proved more complicated in practice, it being necessary to have crews aboard to "fly" it with elevator and rudder control. ZR-1, the Shenandoah, first of three rigids made in the USA, blew loose from its high mast mooring, losing part of the nose in so doing, and fortunately crew aboard were able to nurse her back to Lakehurst. Later the USS Los Angeles, ZR-3 (LZ-125, the ship Zeppelin made just before Graf Zeppelin) did an amazing headstand on its high mast--a cold air mass came in from the sea while its tail was pointing that way, so the high buoyant lift displacing the colder air levered it up to a near vertical attitude, then it settled on the opposite side. This kind of mast "kiting" is something I've seen pictures of modern blimps doing too. The damage from going vertical was minimal in LA's case, but this led to the USN developing the low mast or stub mass--and that I believe is the only mast any Zeppelin design ever moored too (except LA which was in American hands and built to US specs more or less). I might be forgetting something, but I do know that Dr Hugo Eckener was not pleased with the idea of mechanical ground handling; he went so far as to imply that the USN attempts to automate and mechanize airship handling had some kind of direct connection to Americans losing their airships and made it clear he only trusted human ground handling which he thought was gentler on the airship.
So the "stub mast" was a series of short masts meant to just reach the nose mooring when the bottom of the airship was resting right on the ground or nearly so, the hope being that moored to weights on the tail the ship could swing around the mooring circle but not kite up, also of course it was more convenient to get in or out of the airship when its control car was right there on the ground than to climb in and out the nose hatch.
Eckener I believe tolerated the stub mast as part of handling Hindenburg in to the Lakehurst hangar and out of it again--the mast was on wheels.
To be sure we could replace
@Driftless's remark about "mooring" with marching it out of the hangar (and then they had more handling to do out on the field, they didn't just run them straight out and go) for the same sense--ground handling of an airship is tricky and can be time consuming, and it is true that they didn't generally make lots of little stops like a bus or train, it was much preferred to launch and go a long way indeed.
Regarding flying over sea versus land--airships were at their best over the oceans with their fairly stable thermal conditions and the level surface. Between the wars Eckener liked to operate near sea level when he could, often flying at a lower altitude than the length of the ship, he believed that thermals and gusts could not blow straight down into the sea when you were right near the surface. And of course near the sea one is in almost the densest air an airship can have which means if one has not previously risen and vented out gas, one has maximum lift. (Fun fact, Graf Zeppelin once visited the Dead Sea, which is pretty far below sea level, causing its gas bags to deflate quite a lot, and later boasted he'd taken his airship deeper below the sea surface level than most U-boats ever dived to).
I haven't reread the Afrikaschift article, but IIRC it mentions the issues that airship had trying to fly over the Sahara by day, and central Africa in the tropics generally; over land one meets lots of thermals, and these were nasty to deal with. The loss of Shenandoah was blamed in part on sending what was meant to be an ocean going ship over the volatile weather continental USA for PR purposes--though later the Akron was lost in gusty weather over the open Atlantic, and the USS Macon similarly lost her tail fin and was lost over the Pacific.
"Flying the weather map" was how Eckener described his method of covering ground miles ASAP, and could exceed a hundred knots or more with the right tailwinds he devoted himself to locating ad hoc as he went along.
The record airspeed attained by any airship was I believe a USN blimp sometime in the '50s or very early '60s, it is an unofficial record (80 knots) because they did a lot of unapproved stuff to achieve it. Macon I believe was rated up to 75 knots or so, Akron to 72, but standard cruise speeds were lower. Aside from engine power and prop efficiency and streamlining (the last two Navy rigids were beautifully streamlined, their helium inflation allowing for engine rooms to be set up within the hull leaving only propeller outriggers and the control gondola outside it) the limit on airspeed is largely structural; the faster one goes the worse the bending moment from gusts is, so souping up the power is counterproductive.
I do think the interwar rigids were somewhat faster in airspeed than the wartime models. As noted most late war Zeppelins were "height climbers," designed with ultra light structure so they could rise very high and proceed toward England to bomb there, at altitudes where it was hoped the British could not intercept or hit them with AA fire.
The German practice was to fill up an airship with hydrogen on the ground until its cells were taut, and then, dropping sandbag ballast, rise, with the automatic pressure relief valve releasing gas as it expanded; this meant lift would drop and to sustain the rise more sandbags or water ballast would be dropped, thus the gas cells remained fully inflated through the ascent. Only on descending to return to base would they collapse under the rising pressure at lower altitudes.
The height climbers were designed to make their design airspeed at high altitude, and aside from air dynamic pressure being higher at a given speed at a lower altitude, the engines were also overdesigned so as to deliver the necessary power when running on the thin upper atmosphere air; running them at full throttle near sea level would deliver too much power and could easily wreck the ship.
Whereas, hoping to operate near sea level, the postwar civil airships were more robust, though Eckener certainly was able to take the Graf Zeppelin pretty high when he needed or wanted to.
So there isn't really an absolute answer to the question of how fast an airship could go, in ground speed terms; in airspeed it rose from 40 knots toward 70 postwar. 40 knots, the ballpark of Shenandoah's normal performance was too slow to overcome fairly common headwinds.
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