1.what do you man by local transport? Bus-tram is NOT included. However, many touristy towns in the Swiss give their guests free passes for local transit-limited area.
Also note that the pass is NOT valid-will only give discount-on the private upthemountains railways south of Interlaken-making them expensive in stead of very expensive. You do not need to activate passdays for that-just show pass when buying hese tix-they have seen it zillions of times there. There may also be more local ticketing options-these may vary with season.
Further possible discounts are shown in country info. Do not expect too much from that though-except these discounts on some other railways (Swiss has 40-50 different ones)
2.YOu can take on trains anything you want/like, as long as its not too bulky and its very common to see parents with (very) young kids.