２） the が in 困っている人がいたら迷わず助けてあげる Is this a mistake?

1. I think the の in that sentence is an emphasis. So 働きたい is also ok. 2. The が is a particle and the い is いる。 　いる + ～たら = いたら If there is someone in trouble, I will help him/her without hesitation.

2，Your mistake is to connect が and い. Let's separate into words. 困って　いる　人　が　い　たら　迷わ　ず　助けて　あげる。 が→格助詞(かくじょし) thisがshows that 人 is Subject. い→います(verb) You know, Japanese verb is changing. Because of たら, います changed to い.

Heres the full sentence in the book.