MS Vehicles are run in the morning until about noon. The CM that runs the vehicles are also trained at Turnstiles and/or Steam Trains and has the potential to be pulled if the need were there due to call ins...so there is a potential that they may not be operating.
You can not take a park stroller on the vehicles, personal stollers can be taken on if they can fold and are not too bulky (ie: an umbrella stoller is not an issue).
The vehicles pick up in front of the train station (there is a marker on the light poll) and drop off in front of the castle (again there is a marker on the light poll). The Omni bus is a one way trip to the castle, all others can be boarded on either end.
This does not include the horse drawn trolley. That is run by the CM's from the Tri Circle D Ranch and is out everyday again until about noon. It operates based on weather and track work (they have been doing a lot of work on the trolley tracks recently). And it is also used for the Entertainment Trolley Show throughout the day so it may not be taking passengers at certain times in the morning.