Because both trigger at the same time, it depends on who controls each. The triggers will be stacked in APNAP order.
If you control both permanents (which I assume you do), you can stack them however you like. Faultgrinder can be exchanged for something, then its new controller must sacrifice it.
Yes, you control that trigger. It doesn't matter who, if anyone, controls Faultgrinder at the time that trigger is put on the stack and/or resolves.
EDIT: To clarify: Whoever put Faultgrinder into play chooses which land to blow up.
I'm curious about how this works also. I understand what you're saying, but let's take a look at how these abilities stack. The cards I'll use for this example are Walker of the Grove (because it doesn't have a comes into play ability and its leaves play ability works well with this), and Confusion in the Ranks.
With Confusion in the Ranks in play, you play Walker of the Grove by paying it's evoke cost. When it comes into play, two abilities are triggered, the 'sacrifice' for evoke trigger and the 'exchange' for Confusion in the Ranks trigger. As the controller of both abilities and the active player, you place all of your triggers on the stack first in the order you choose. Assuming you put the trigger stating "When Walker of the Grove comes into play, if its evoke cost was paid, its controller sacrifices it." on the stack first followed by the trigger stating "Whenever an artifact, creature, or enchantment comes into play, its controller chooses target permanent another player controls that shares a type with it. Exchange control of those permanents.", the second trigger will resolve exchanging control of the creature with one of the same type an opponent controls.
The next part is the one that confuses me, you control the ability stating "When Walker of the Grove comes into play, if its evoke cost was paid, its controller sacrifices it.", though you don't control the creature anymore. Because of the wording on evoke, does the 'sacrifice' ability force your opponent to sacrifice the creature even though the controller of the ability and the controller of the permanent are not the same, and I assume the result would be different if evoke instead stated, "When ~ comes into play, if it's evoke cost was paid, sacrifice it." (the ability doesn't reference the controller of the creature so the controller of the ability would be the only thing it has influence over).
If you control both permanents (which I assume you do), you can stack them however you like. Faultgrinder can be exchanged for something, then its new controller must sacrifice it.
EDIT: To clarify: Whoever put Faultgrinder into play chooses which land to blow up.
With Confusion in the Ranks in play, you play Walker of the Grove by paying it's evoke cost. When it comes into play, two abilities are triggered, the 'sacrifice' for evoke trigger and the 'exchange' for Confusion in the Ranks trigger. As the controller of both abilities and the active player, you place all of your triggers on the stack first in the order you choose. Assuming you put the trigger stating "When Walker of the Grove comes into play, if its evoke cost was paid, its controller sacrifices it." on the stack first followed by the trigger stating "Whenever an artifact, creature, or enchantment comes into play, its controller chooses target permanent another player controls that shares a type with it. Exchange control of those permanents.", the second trigger will resolve exchanging control of the creature with one of the same type an opponent controls.
The next part is the one that confuses me, you control the ability stating "When Walker of the Grove comes into play, if its evoke cost was paid, its controller sacrifices it.", though you don't control the creature anymore. Because of the wording on evoke, does the 'sacrifice' ability force your opponent to sacrifice the creature even though the controller of the ability and the controller of the permanent are not the same, and I assume the result would be different if evoke instead stated, "When ~ comes into play, if it's evoke cost was paid, sacrifice it." (the ability doesn't reference the controller of the creature so the controller of the ability would be the only thing it has influence over).
[c=Black Lotus]Lotus[/c]=Lotus
[c=Black Lotus|Alpha]Lotus[/c]=Lotus
[mana]WUBRGS-TQ-1-2-12-XY[/mana]=WUBRGS-TQ----XY
[mana]{WU}{UB}{BR}{RG}{GW}{WB}{BG}{GU}{UR}{RW}{2W}{2U}{2B}{2R}{2G}[/mana]=(W/U)(U/B)(B/R)(R/G)(G/W)(W/B)(B/G)(G/U)(U/R)(R/W)(2/W)(2/U)(2/B)(2/R)(2/G)
Triggered Ability-Whenever/When/At ..., (effect)
Replacement Effect-If/As ..., (effect)