Is there a way for me to add tags to someone else's questions so that they get looked at?
No, only the one creating the question and site administrators can tag others' questions
Please up-vote Personal Tagging which is about opening this up so we all can tag.
or when I respond to them and want to add a tag can I do that?
You can of course write whatever you want in your own comments
I tried to do this for a short period. See more in this comment.