I will be staying near the Tiananmen Square. Is the Summer Palace within walking distance? Otherwise what is the best way to travel there?

No, it is not within walking distance; actually, around 20km from Tiananmen Square to the park. Walk from the square to Tiananmen East metro station to take subway line 1 to Xidan, where transfer to line 4 to get off at Beigongmen. Then u can easily walk to the royal garden.

To the Temple of Heaven, the distance is 3-4km, hard to walk there. Then you can take subway line 1 at Tiananmen East to Dongdan, where transfer to line 5 to get off at Tiantandongmen. Getting out of the station, you can easily walk to its East Gate.