Helping her move a table is one thing. You are out in public (the stairs and hallways) and you are briefly in HER space.

Using your Internet is different -- she has to be in YOUR space for this, and presumably you will give her some privacy.

No, I would not go that far with someone I don't trust, with someone I am not friends with. She will have other folks to ask for the Christmas call -- she must have friends, and asking you because . . . you are close by? She doesn't have to go outside, drive etc.

And if she has no "friends" she can ask well, that is her issue.

No, I would just say with the holiday and such it is not convenient.