White paper with black printing is worth slightly more to karung guni that mixed paper waste and coloured paper because it gets a slightly higher price at cash for trash. It is easier to recycle white paper into new paper. The black ink comes off during the recycling process. So does correction fluid, tape, and staples.

Is my paper considered black and white if it has pen marks on it?

Yes.

The term “black and white paper” is a generic term and includes various grades of white ledger paper. 

Local recyclers have informed us that if your black and white paper has pen marks, it is still considered to be in the generic “black and white” category. 

As long as it is ink, marker or pencil (as opposed to crayon or oil pastel) and that the coverage isn't extensive (handwriting is fine, an entire coloured in picture is not!), then it is fine to include the paper as black and white.