One day visiting to Hanging Monastery & Yunggang Grottoes

As for your questions, here is my suggstion:
1. Yes, you can take a bus. But if you have a group of people, it is suggested to hire a car. If you travel on your own, it is suggested to join a local one day tour to visit the two places in one day.
2. To reach the monastery, it costs around two to three hours on the way. To visit the temple, it costs around one to one and a half hours. To visit the Yungang Grottoes, it costs aroudn two to three hours.
3. From railway station, you can take a taxi to reach local bus station on Pingcheng Street to take bus to reach the Hanging Monastery directly.
4. From the monastery to grottoes, there are no direct buses, so you need to go back to DT first and then take a taxi to reach Xinkaili and change to bus line 3 to reach the grottoes.
5. I'm afraid there are no pure vegetarian restaurants between.