Admire Beijing by sub way.

I think it may be hard for u to cover all the places you mentioned in two days.

For the first day, you can go to the Great Wall first. To reach the Wall, you need to take the public bus line 919 to reach the Great Wall directly. Back from the Wall, you can visit the Houhai area, you can visit the Beihai Park and Houhai Hutong area. The local subway line 6 can take you to reach Beihai North Station. Get out of the station, you can see the Beihai and Houhai parks. Then at night time, you can go to the Sanlitun Bar Street. The subway line 10 can take you to reach Tuanjiehu Station. Get out of station, you can walk along the Gongrentiyuchang North Road to reach the Bar Street.

The next day, you can visit the Forbidden City and Tiananmen Square in the morning. These two places can be reached by subway line 1 and u need to get out of the station from Tiananmen East Station. Then you can take the subway line 1 to reach Xidan Station, where you can change to line 4 to reach the Beigongmen Station. Upon reaching that station, you can walk to reach the Summer Palace. After that you can take the subway line 4 to go back to Xizhimen Station to change to line 2 to reach Yonghegong Station. Get out of the station, you can see the Lama Temple. Then if time is enough, you can take the subway line 5 from Yonghegong Station to reach Tiantan Dongmen Station. Then you can walk to reach the Temple of Heaven.

For other places, I do not think you can cover because of the limited time.