Is summer palace in Beijing closed on march 2015?

No, it isn’t. The place opens from 07:00 to 17:00. The ticket price is CNY20.
Here is my suggestion for your trip:
March 20: hotel check in; Tian’anmen Square
March 21: Bird’s Nest; Water Cube; The Summer Palace; Yuanmingyuan;
March 22: Badaling Great Wall (daytime); Sanlitun Bar Street (nighttime);
March 23: Forbidden City; Shicha Lake; Wangfujing Street; Silk Street; Chaoyang Park;

Wish you have fun!

Thank you. I will arrive at beijing at 7 p.m. is tiananmen still open at 7 p.m?

Of course. It is a square, open to the public for 24h. Upon landing, you can stioll have a good sightseeing around.

Tiananmen is not a square, but the "gate of heavenly peace". Tiananmen Guangchang is the related square ("Square of the Gate of heavenly peace"), which is open 24 h as Nancy said.