As I recall, he was only about the twentieth or so self-declared Mahdi in Sudan in his century. That particular heresy was pretty wide-spread - or it was just a battle cry for standing up against the foreign regime, more like.
Interesting, the German East African state didn't come up in any of what I read. To the extent that you can believe what people say in parliamentary debates (the Hansard was one of my main sources), the immediate spur to action was the Italian defeat at Adowa, plus some Conservatives, (including Henry Morton Stanley) simply figuring there were interesting resources to be had in Sudan - cotton, say. The mindset in 1896 was quite different from what it had been back in 1884-85, when indeed the only thing that interested the British in Sudan was called Charles George Gordon.
Salisbury himself wasn't too much of an imperialist, either, or at least not in that part of the world - I too had noticed the irony of all that expansion occuring on first Gladstone's and then his watch. As for Fashoda, that whole thing started long after the British began their conquest (it took them nearly three years, not because the opposition made them break any sweat but because they didn't want to outpace the railway they were building). So no, the French had nothing to do with the initial conquest plans - I'm just saying, while they were already there anyway and so close to completing their railroad plans, they were hardly going to let some French explorer waltz in and sabotage it all at the last minute.
And yeah, the Nile water story... the English were pretty clever about that, and not above threatening Egypt with precisely that, whenever it suited them.