There is no period seperating different parts of an ability, unless you mean seperating "paying the costs of the ability" and "the ability itself." You can't pause partway through resolving a complicated ability, just like you can't pause in the middle of a Timetwister or other multipart spell. The whole thing resolves at once, or none of it does - no player has priority during the resolution of a spell or ability.
But you probably meant "between paying costs and resolving abilities" and yes both players get priority between those two actions. In the Top case, the cost is to tap it, and the ability goes on the stack, and then you can respond with Shrapnel Blast.
Let's look at [card]Gemstone Mine[/card]'s official text (always use
gatherer.wizards.com):
, Remove a mining counter from Gemstone Mine: Add one mana of any color to your mana pool. If there are no mining counters on Gemstone Mine, sacrifice it.
Unlike Top, this ability is a mana ability, which can't be responded to (or countered but that's not relevant here). Also, the sacrifice clause is
part of the mana ability, not a seperate triggered ability (contrast this with [card]Serrated Arrows[/card], which has a sacrifice ability that is
not part of its remove-a-counter ability).
So no, your play was wrong; because the sacrifice is part of the mana ability, getting the mana and losing the land are essentially simultaneous. You do technically get the Mine mana first, but you're not able to spend it on the Crop Rotation until the Mine is gone (the ability finishes resolving).
Moreover, even if you had the Mine and a Forest to pay for the Crop Rotation, it still wouldn't have worked, because you can't respond to a mana ability (even the ones with restrictions on when you can use them like [card]Lion's Eye Diamond[/card]).
