第一句应该改为：
We sang English songs and did some Chinese dances last night.
因为"and"连接的前后两个分句的关系并列,所以时态应一致.
第二句应该改为：
LOOK,your pen is on the ground.Pick it up.
一般像pick up这样的短语,如果对象是一个短语,则放在介词之后（例如：Look,some pens are on the ground.Pick up the red one.)；若对象只是一个代词,例如it,him,her,me,them,us等,则把它放在动词后、介词前（例如：Look,some pens are on the ground.Pick them up.）