1. By context I believe that Rudyard Kipling means that The White Man's Burden IS the Imperialism. "No iron rule of kings, But toil of serf and sweeper, The tale of common things....." Here Kipling states that people are going through change in government from theirs to a now Industrial type classes (High, Middle, and Low) He also mentions that from once you were noble before the Imperialism of your country now you are to toil with serfs and sweepers (Lower classes).
2.) He in the last stanza's justifies Imperialism. He states to "Have done with childish days- The lightly-proffered laurel, The easy ungrudged praise." This is possibly the outcome of when a citizen that was in their country when it was Imperialized and now is has adjusted fully and is coming through it proud.
3.) It could be appealing to anyone that if they are even in the hardest situation like for example Imperialism (Your whole country changes). Your life could change and if it does go for the bad if you try hard enough to adjust you can adapt into a healthy and wealthy lifestyle once again.