Little Mürren has three "stations." When you haven't been there, it is indeed confusing. When you're actually there, it's very clear.
Mürren BLM is the one that gets the train from Grutschalp, which in turn gets the cable car from Lauterbrunnen (across the street from the Lauterbrunnen train station). These rides (Lauterbrunnen to Grutschalp to Mürren) are all coordinated, and at each change you just follow the crowds.
Mürren Schilthornbahn is the one that gets the cable cars, down to Gimmelwald and then Stechelberg, or up to Birg and the Schilthorn. From Stechelberg, you can get a bus to Lauterbrunnen, or it's a lovely walk taking about 1.5 hours. You should do at least part of this walk while you're there; it's a perfect activity, as Rick says, for the "cloudy day, weary body, or tight budget." Plus, you can do as much of the walk as you want, then catch the bus the rest of the way.
Mürren Allmendhubelbahn is the one with the funicular up to Allmendhubel; no further connections. This is a great thing to do, as the ride up the Allmendhubel is much shorter and cheaper than the Schilthorn, but you get great views of all three peaks and a lovely park area to walk around; there's even a restaurant.
Yes, if you have a Swiss Travel Pass, you don't need to buy tickets or make reservations for any fully covered rides. You just board, and show your pass when tickets are checked. However, for any rides not fully covered (such as the Jungfraujoch, or the Wengen to Maennlichen cable car), you have to buy tickets BEFORE boarding; show your pass to get the appropriate discounts when buying the tickets.
I can't emphasize enough that I know transit in this region seems confusing before you get there, but it's really easy once you're there. You can't go through mountains - only up, down, or around them. So, when you can see the mountains, and there are large maps at every station showing the route options, it's easy.
If you use the Swiss Rail website or app, it will give door to door directions for the whole country. For instance, if instead of "Mürren" you put in your hotel's address, it will include walking directions to the hotel; for cities, it includes tram and bus directions and times.