Yes, you can do that. It doesn't matter that the source of the Rats' ability no longer exists by the time you're done activating it, because you didn't do anything illegal during its activation. The ability will go on the stack as something separate from its source, like always.
Basically, there isn't any rule in the process of activating an ability that checks if the source is still there. Since that rule doesn't exist, it doesn't matter whether it's there or not.
Does morph work the same way? For example, could I pay the morph cost of Skinthinner in part by sacrificing it to Ashnod's Altar?
I would guess no since morph is a special action that doesn't use the stack. It simply happens instantaneously
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Does morph work the same way? For example, could I pay the morph cost of Skinthinner in part by sacrificing it to Ashnod's Altar?
You can do that, but I really wouldn't recommend it. Skinthinner has a triggered ability, so if you sacrifice it while you're paying its unmorph cost, the ability will never trigger (since it's already dead).
EDIT: HugSeal, it's true that unmorphing is a special action, and doesn't use the stack (in other words, resolves immediately) but it still follows the same procedure for paying costs. You're allowed to use the mana ability of Ashnod's Altar while paying the cost, so the Skinthinner is already in the graveyard by the time it would be turned face up.
Could I announce the Rats' ability for 3, then activate Soldevi Adnate's mana ability, sacrificing the Rats, in order to pay for it?
Basically, there isn't any rule in the process of activating an ability that checks if the source is still there. Since that rule doesn't exist, it doesn't matter whether it's there or not.
Does morph work the same way? For example, could I pay the morph cost of Skinthinner in part by sacrificing it to Ashnod's Altar?
I would guess no since morph is a special action that doesn't use the stack. It simply happens instantaneously
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You can do that, but I really wouldn't recommend it. Skinthinner has a triggered ability, so if you sacrifice it while you're paying its unmorph cost, the ability will never trigger (since it's already dead).
EDIT: HugSeal, it's true that unmorphing is a special action, and doesn't use the stack (in other words, resolves immediately) but it still follows the same procedure for paying costs. You're allowed to use the mana ability of Ashnod's Altar while paying the cost, so the Skinthinner is already in the graveyard by the time it would be turned face up.