◆句中more and more作什么语法成分？

more and more是 程度副词，相当于increasingly，做状语，修饰out of hand。

 ◆为什么可以用在介词短语out of hand前呢？

下面的例句可以解释这一点：

In my first year at college my drinking got completely out of hand.    (Cambridge Advanced Learner's Dictionary)

Things got a little out of hand.  (Cambridge Advanced Learner's Dictionary)

 The children are completely out of hand.孩子们完全不受管束。(《麦克米伦高阶英汉双解词典》

The football fans have got completely out of hand.  （《牛津高阶英汉双解词典》）