Do I use inverted quotations when the question asks me to 'pick out phrases' or 'use evidence from the passage' to support my answer?

It depends on the requirements of your syllabus. What have you been taught in school?

Okay then. You should defnitely use inverted quotations when quoting phrases or words (depending on the question) directly from the passage. However, if you are paraphrasing an idea introduced in the passage then you do not need to use inverted quotation marks.