句子分析I saw a lot of children playing in the garden,most of th

英语句子不同于汉语句子,两个独立的句子之间必须有连词连接,不能两个句子就那样放一块
这个句子已经有一套谓语了see,就不需要其他的谓语.如果你用were,这就是两个句子,中间必须有连词,比如：I saw a lot of children playing in the garden,and most of them were girls.就是正确的.
这里其实就是一个独立主格结构用法,表补充说明,相当于一个并列句,意思和I saw a lot of children playing in the garden,and most of them were girls一样.

most of them being girls.在这里做状语，如果用were就需要大写成为另一个句子，I saw a lot of children playing in the garden.And most of them were girls.

most of them being girls是分词短语的独立结构形式,是对前面children的附加说明，只能用being.

I saw a lot of children playing in the garden,most of them being girls.
这是see sb doing sth的结构，看到某人做某事
如果用were是宾语从句，语法上也没有错。