You are correct.
"I went hiking on three Saturdays in a row" is a correct sentence, but doesn't specify how long ago those hikes were.
If you want to add that information, you could use
I went hiking on the last three Saturdays
or:
I went hiking on each of the last three Saturdays
Our hope has diminished.
Nothing wrong here. We use the word diminished with emotions often, particularly when the diminishing emotion is positive. When things are getting better, though, we might not be as likely to say, "Our despair has diminished", instead saying something more like, "Our despair has lifted."
Please diminish your voice.
Definitely not. As individuals, we lower our voices, not diminish them. That said, I think it would be okay to talk about crowd noise diminishing. We walked away from Times Square, and the voices diminished. I wouldn't have any problem with that sentence.
Our sugar supplies have diminished.
You may notice I took the liberty of substituting storage with supplies. Storage doesn't diminish, but supplies can. That said, my revised sentence seems to have a very formal register. I would never say that in my own kitchen, but an executive in a chocolate factory might: "Our sugar supplies are diminished; if the trucks don't get here with a new shipment soon, we'll be forced to shut down the production line."
The flooding has diminished in our area.
This is a tricky one. It seems grammatical, but I don't like it – probably for idiomatic reasons. I think I would say instead, "The flooding has receded in our area", which is a more descriptive word, and one my ears are used to hearing being used with flooding.
Diminished means, "to make or become less," but your question brings up an interesting point: that it can sound very awkward when applied to the wrong thing, such as misery, or flooding, or the volume of our music.
Best Answer
Exactly is an adverb, so you can not use it to modify a noun (tasks). That means your first sentence is not grammatical.
You have two options:
As @StoneyB points out, the second option can be ambiguous.
In the first sentence, exactly clearly modifies which, but in the second one, it seems to modify perform. If it modifies perform, you're asking which tasks should be performed with great(er) accuracy. The second sentence can, however, also be read as if exactly modifies which, just like in the first one. In that case, the adverb just moved to the end of the sentence, more or less as an afterthought. One might add a comma in that case:
In most cases, I think the second sentence would be interpreted as meaning the same as the first.