Is the entrance to the Hohle Fels cave possible by just 'walking in'
When I visited the cave it was possible to just 'walk in'. There is no museum or visitor centre (there are plans to build a visitor centre), just one or two people who give some explanations or offer a guided tour if someone is interested (in German only). The cave isn't very large, though it is the largest of the six inscribed caves. Seems, that currently the cave is open also on weekdays.http://www.museum-schelklingen.de/oeffnungszeiten-fuehrungen
The coordinates in the nomination file indicate the locations of the caves, at most locations you have to walk a few minutes from the parking lot to the cave (see my Review). The archaeopark should be signposted.
How are the public transport options?
I am not sure, because I travelled by car. Trains between Ulm and Blaubeuren should run frequently even on Sundays. I guess there are also busses from the train station in Blaubeuren to Schelkingen, but I'm not sure if there are stops along the Bundesstraße. In the Lone Valley Niederstotzingen is the largest town, I guess.