关于while doing sth的系列疑问

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课文中的句子：

The goal of using different organic farming methods is to grow good food while avoiding damage to the environment or to people's health.

关于while avoiding，加上when doing，if doing，although doing，我的疑问：

1.在英语复合句中，当状语从句的主语与主句的主语相同时，从句可以省略主语，并把谓语动词改为非谓语动词形式：

When doing homework, he often listens to music.

= When he does his homework, he often listens to music.

2.while/when/if/although等引导状语从句时，如果从句主语与主句主语相同，且从句含有动词be，则可以把从句的主语和be同时省略：

When doing homework, he often listens to music.

= When he is doing his homework, he often listens to music.

3.分词作状语时，可以在分词前加上连词while/when/if/although等，本质是分词作状语，而不是状语从句的省略。

请问老师，以上三种说法谁对谁错？

4.按照1和2的说法，从句主语和主句主语相同时才能省略，那么我提问的句子中的while avoiding，省略的是什么主语？

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