Hello! To your questions:
1. Walk eastward from the hotel to find the Dongdi Bus Station. Catch Bus No.4 to Baiyun Road Terminal (Baiyun Lu Zongzhan) to change another Bus 223 which will take you to the cable car station of Baiyun SHan.
2. Huanghua Gang Park is on the way to Baiyun Shan. There is a stop called Huang Hua Gang. You can use Bus 223.
Yuexiu Park, Sun Yat-sen Memmorial and Liurong Temple is not far from each other. You can use Subway Line 2. You hotel is about 1 km from the D exit of Haizhu Plaza Subway Station of Line 2. Liurong Temple is between Gongyuanqian Station and Zhongshan JIniantang (Yat-Sen Memmorial Hall). Then Yuexiu Park is another stop further from Zhongshan Jiniantang.
Chen Clan Academy is a bit further. You can also use Subway Line 2 to Pazhou. The place is in the other side of the river. Suggest you take a taxi to the place directly, about 3-4 km.
Zhujiang Road is close to Subway Line 1 and 3. Zhujiang Road has many parts. That's all I can help. Good Luck!