Yes it is. Mental acuity doesn't mean "how fast you come up with ideas", it's much, much broader and more vague term than that.
No.
It just means it's not covered. D&D's six stats don't measure everything about a PC's capabilities, and thinking that they do is a big part of making a nuisance of yourself as a DM or player, frankly.
What, exactly, is a "good idea". Define that.
Because animals can come up with "good ideas", man. Animals can process information incredibly fast, often far faster than a human. Does make them higher than INT 8? I don't think so.
A good idea which is relatively simple is not something that requires a high INT. This includes plans like sneaking around - again, stuff even animals are good at.
If the plan involves like, complex physics, or knowing exact detailed routes from a map, or memorizing a bunch of numbers or something, or analyzing complex speech or the like, sure, that's probably off but that's not a "good idea", that's a "complex idea", and often those sort of plans are absolutely terrible plans. Just complicatedly terrible.
What is it that you think deductive reasoning means? Because it's a specific mode of thought, and it's not one that's typically used by D&D players when forming plans, in my experience.