What your in essence talking about is being "passive".
It's a common trait that people can fall into being but it poses a lot of problems some of which you highlighted;
It's not really the fact that you cant refuse, its just your internal diaglog in your head is making it hard to refuse as your telling yourself your obliged to help them.
The landlord situation I would probably have done the same but then again if you're leaving anyway and it causes you inconvinience, I would stand my ground to say im unavailable those days. Alternatively if you are available then why not?
As for your friend; if she rings you can says something like that; Its really up to her. As a friend I would help her but then she seems to be a user and I probably wouldnt get those phonecalls because I'm not passive in my day to day interactions with her - this is something thats a bigger problem than these isolated situations which you need to learn to address.