Nothing about your process is quantitative in nature, nor does it require high-purity reagents. So most definitely do not invest in reagent-grade anything. To answer your questions in order:
1) The "heavy powder" calcium carbonate will be sufficient. It may be "clumpy", in which case you will want to physically break it up prior to mixing it in with the water. You should wear rubber gloves and a dust mask if you need to do this. The only purpose of this compound in your procedure is to raise the pH.
2) You definitely do not need anhydrous or dried calcium chloride. You are not trying to quantitatively measure out this compound and you are just going to put it in water anyway, so hydration is not an issue for you at all. The purpose of this reagent (generic term, not referring to any "grade" or purity) is to provide chloride ions, that at high pH will form a layer of cupric chloride, which is green when it absorbs water from the air to form cupric chloride dihydrate. Again, this will be a product of your procedure and the degree of hydration of the calcium chloride is not relevant. As in step one, this compound may be clumpy and if so you should break it up as described there.
3) The phrase "should be granular or granular reagent?" is the key. As stated above, there is no need for reagent grade materials for your process, so if your options are "granular" vs. "granular reagent" then just get the granular, not the granular reagent ;) The role of this compound is to both raise the pH and to provide chloride for the purpose described in step 2.
Again, it may be tempting to think you will get a better patina by investing in expensive reagents, but for your process that would simply be a waste of your money to buy reagent-grade anything if there is a lower grade alternative.