How do I travel to Changbai mountain and heaven lake from Changchun?

You may take a bullet train to Antu West Railway Station from Main Railway Station (about 2 hours). Next, walk to Antu Railway Station (within 10 minutes). Then, take a bus to Erdaobaihe Town (about 3 hours). Upon arrival, take a taxi to the mountain for about CNY 60. You can see the lake at the mountain.

Yes, you can stay overnight there. You may consider the Changbaishan Landscape Resort Hotel. It is adjacent to the entrance, so you can easily find it. You can book a room by dialing at 86-0433-5052222. ;)