Trains and Didi and Hotels

Hello, I'm going to be going to China in a week. I'm going as part of a study trip, and at the end of it, I will have a few days to myself, where I'm planning to go up from Shanghai to Jinan, where I'll be staying. While I'm there, I am planning to climb Mount Tai and see the local springs. And I'm leaving early at 7:15 AM a few days after from Jinan Yaoqiang.

My question is regarding transportation and I don't really speak much Chinese, nor do I have any Chinese friends I'll be with. I'm planning on buying tickets from Shanghai to Jinan and also train tickets from Jinandong to Taishan station or Jinan to Taishan station. Is it recommended to book these tickets as soon as possible or wait until the day of? Also, since I don't know when I'll finish climbing Mount Tai, I don't want to book the ticket until after I'm done climbing for fear of booking too early and missing the train or booking too late and being stuck in Tai'an for hours. How should I proceed?

Also, can I book a Didi for 4 AM? I looked up on Google and it said some people have gotten their rides as early as 5.30 AM, but I'd really rather be at the airport as early as possible. How early can I book? Worth noting I'm planning on getting a hotel near the airport (under a thirty-minute drive). I have some hotels in mind, but for those who have traveled to Jinan before, do you have any recommendations for hotels next to the airport?

Sorry if this comes off as me rambling. I've never traveled by myself like this before and I wanna make sure I don't screw myself over. Thank you for your time :)

If it makes it easier, I could post my tentative itinerary.