What are the plugged pipes on the outside of my roof staircase wall?
yes, that's odd.

However, while they are copper pipe usually used for water lines, their location (outside, 'roof' area, stairway on other side indicating no ability to place a water related item there) suggest to me that they have another purpose.

I believe that these were ad-hock brackets to provide attachment and support of some object. My first guess would be a satellite dish.

No matter the old purpose, they do need to be water tight. However, that is an issue for your landlord and I don't think that you have any worries.