The game they enjoy most is the underwater tricycle race. This takes place seven feet under water and, while some children pedal their tricycles, others push or pull them.

1.  and 是并列连词，引导连接并列分句。也就是说：

This takes place seven feet under water 和  while some children pedal their tricycles, others push or pull them.  是由 and 连接的两个并列分句。

2.  while 表示“让步或对比”，引导的句子放在开头是从属连词，放在后面是并列连词。

这两句都可以说：

while some children pedal their tricycles, others push or pull them. （while 是从属连词）

some children pedal their tricycles, while others push or pull them. （while 是并列连词）