I'm sorry you're struggling with holding your boundaries right now. I think it's reasonable to say no. And I think it's reasonable that you have said no.

I would just ignore the coworker causing trouble. She sounds unimportant.

Regarding your roommate's depression, it will not be effective to tell any person with depression to just get over it or call them a big baby. I understand the desire to want to say that, but depression can be just as serious as cancer. One does not just get over it. In fact, that kind of judgment will likely not help her heal. Depression is an illness that requires treatment. She can no more get over depression than your father could get over his cancer.

To enforce your boundaries I think it would help to move beyond a text conversation to a real conversation where you explain to her that you don't have the capacity to care for her son or assist in that. You're renting a room and that's the extent. Take a few minutes to have the conversation to let her know in person what the terms are. That might help.