Tone is the author's attitude toward the speech. Since we know that Dr. King was the author and presenter of the speech, this was one of inspiration, seriousness, hope, and encouraging. This is not to be confused with mood. Mood is your feelings from the text. So, while the tone may be one of hope, to say it was 'hopeful' would be a mood (if that is indeed what you are feeling when hearing it.)
By standing by his side and pushing him on.
The last one - the others imply that the rain is walking down the street
