A passport is a thing you get given, so you can't 'prepare it'. Did you mean application? You also need a 'have' in there. I will submit​ my passport application ​as soon as I have prepare​d it. In your second one, I'm not sure what you mean. Can you write it a different way? What context are you thinking about?

Nadia was trying to help, but not really succeeding. There were many mistakes in what she wrote.

Thank Nadia Tretyakova' explanation,I have understood.

Please be free for more days. if you want a person to be free for some more days, you will use a constraction: Could you find a spare/free time for more days? sometimes native speakers use "spare" instead of "free". Spare time is the time left over when other things get done. e.g.: If I finish early I have spare time Free time is time I have because I have not planned any activity for that time. E.g.: Sometimes I have free time because I decided not to do something. Spare time is a subset of free time. All spare time is free time but some free time is not spare time. I prefer to use "spare", when we speak about time. P.S. in your example we can understand "free" as a "cheap"/"with no price"