None of them are grammatically correct because none of them are complete thoughts let alone sentences.

All three try to specify the particular monkey by enumerating that it can see your ears but do no more.

Take away the description of the monkeys ability to see your ears and what you’re left with is “the monkey”.

“The monkey” isn’t a sentence.

If you are the subject and what’s happening is that you’re wondering if the monkey can see your ears then the sentence you want is “I’m wondering if the monkey can see my ears.”

If, as I suspect, you’re using “the monkey whose ability to see my ears I’m wondering about” as the subject of some larger more complex and cool sentence then you gotta lay out that part before someone can give solid grammatical advice.

Not a native speaker but the last one, using ‘it’ instead of ‘they’ would sound the most natural to me

“The monkey about whose ability to see my ears I’m wondering”.

Part of the issue is that the thing you’re wondering about needs to be a noun, but the verb “can” doesn’t have an infinitive or gerund form (that is, there’s no purely grammatical way to convert it to a noun, like *“to can” or *“canning”). We generally substitute some form of “to be able to”, but it’s not something our brain does automatically.

Also, there’s an implied pragmatic context that some of the other comments seem to be overlooking:

• The speaker is apparently replying to a question asking them to indicate one monkey out of several possibilities

• The other party is already aware of the speaker’s doubts about a particular monkey’s ear-seeing ability

• The reason this doubt is being mentioned now is to identify the monkey, not to express the doubt.

If your wondering isn’t critical to the thought I would simplify to “the monkey who might be able to see my ears” or “can possibly see my ears”. Otherwise AbouBenAdhem has the best option, though I might also suggest “The monkey whose ability to see my ears I’m wondering about”; splitting the prepositional phrase is more strictly proper but I think it reads a little better like this.

They do all sound stupid.

As it’s a complete statement just say “I’m wondering if the monkey can see my ears.”

Because it is ‘the’ monkey, rather than ‘a’ monkey, it is implied that the monkey has already been referred to.