Hi happyinti -
I've not done those hikes.
The usual walk from Mürren to Gimmelwald does not take 2-3 hours; it is only about 2 km on a reasonable trail.. I do not know the via Ferrata. And, there are frequent cable cars.
These maps may help.
The Switzerland mobility map goes right to Rotstockhütte if you use the name as a search term.
map.wanderland.ch/?lang=de&route=all&bgLa yer=pk&resolution=1&la yers=Wanderland&E=2630 654&N=1154951
I note that the trail through the Rotstockh252tte as shown on that map is a heavy green line ( although dashed).
That means that you can get further information about that trail by clicking on the trail line.
If you do, you will learn that is a named National Trail, the via Alpina, stage 12. (The map sometimes responds slowly when searching. Be patient.)
Click on the small name tag, and you should get the window shown in the attached screen grab.
Click on "More Information."
You will get to a page with height profiles, hiking times ( for the whole stage) , etc., etc.
(Second Screen grab.)
The height profile shows that the climb from Mürren to Rotstockhütte is about 400 meters altitude change over about 7 km distance.
The other very detailed map that I sometimes use is SwissTopo:
map.geo.admin.ch/?topic=ech&lang=en&bgLa yer=ch.swisstopo.pixel karte-farbe&layers=ch.bav.ha ltestellen-oev,ch.swisstopo.swiss tlm3d-wanderwege&layers_visi bility=false,true&X=15 4951.92&Y=632064.49&zo om=6
I have turned on hiking trails. They follow the normal color conventions. Red means mountain trail. Blue is technical climbing, yellow is the easy kind that does not require any equipment..
I have not hiked cabin- to-cabin, but I understand that they need advance reservations during good hiking weather.
will tell you that if you come by train from Interlaken Ost, you will arrive at Lauterbrunnen at 1225. That is an easy connection for the 1238 cable way to Grütschalp. you will get to Mürren by 1258. Next trip is at 1308, arrival at 1328.
You know better than I do about your hiking capabilites, but you could always ride to Gimmelwald instead of walking/hiking.