As to whether mentalese has a grammar, as far as I can tell the idea of grammar itself is not really a fundamental truth of language, but more like a concept we added in order to explain how words are used. In that sense I do think mentalese has a grammar, because you can explain things the same way that you explain the grammar of regular language. Imagine seeing a set of five crazy monsters that you didn't have a name for, and then you see one of them emerge again, and you recognize it as one of the monsters you've already seen. In a sense that is a "noun" concept in mentalese, because it's corresponding to an object. Or perhaps you see the monster move in a way that isn't quite jumping and isn't quite running, you're sensing a "verb" concept, aren't you? And so on.
As to whether language is intrinsic, it certainly seems like language is intrinsic to the modern human experience. But is it really intrinsic to humans? Just as a thought experiment, too barbaric to run in reality. Imagine letting a group of a few dozen humans grow up without any contact with language and the modern world. Are you confident they would develop language? I'm not sure, personally.
I am entirely certain that those humans brought up with no contact with language would figure out language for themselves. Consider, for example, deaf children who were raised in the time before sign language was common. Those children consistently found a way to communicate. It may not be exactly like the language we use or be as complex — but it is language.
It's worth adding that there are two definitions of grammar which can result in misunderstanding and crossed wires. There's the prescriptive definition, more familiar to laypeople, which is "rules" like 'no split infinitives' and 'don't start a sentence with and' and so on. These were largely developed to constrain language. The other definition of grammar is moreso the intrinsic rules natural languages follows, ie syntax. I work on the latter and we would call it a fundamental part of language (language = alphabet + grammar) - it's basically patterns which form language that we can't easily explain, but we know that 'teapot nineteen boy the bounced several' doesn't follow them, and nor does 'threw stairs down a teapot did John', even though we can infer an intended meaning. (This is where the idea of universal grammar comes from, but they're not the same thing).
As an aside, thiis kind of grammar can apply to what people wouldn't consider languages; eg animals aren't considered to have language, but communications like bee dances and bird calls have been found to follow some underlying 'grammar'
As for the thought experiment, the closest I can think of is case studies of feral children and the like (caveat: highly criticised for reliability for various reasons). There is also some work on when human ancestors first developed language and which cognitive/behavioural developments it coincided with; to my recollection it was related to more complex organising of group members (eg you do x, then I'll do y, and later we do z with so-and-so) and also I think there are strong links to imagination and storytelling (pinch of salt, though, my memory is foggy on this)
If you are interested in FoxP2, two articles worth looking at:
https://www.cell.com/fulltext/S0092-8674(09)00378-X
https://sciencedirect.com/science/article/pii/S0306452210015332
I think they are paywalled but I'm sure you are resourceful enough to bypass trifling annoyances.
As to whether mentalese has a grammar, as far as I can tell the idea of grammar itself is not really a fundamental truth of language, but more like a concept we added in order to explain how words are used. In that sense I do think mentalese has a grammar, because you can explain things the same way that you explain the grammar of regular language. Imagine seeing a set of five crazy monsters that you didn't have a name for, and then you see one of them emerge again, and you recognize it as one of the monsters you've already seen. In a sense that is a "noun" concept in mentalese, because it's corresponding to an object. Or perhaps you see the monster move in a way that isn't quite jumping and isn't quite running, you're sensing a "verb" concept, aren't you? And so on.
As to whether language is intrinsic, it certainly seems like language is intrinsic to the modern human experience. But is it really intrinsic to humans? Just as a thought experiment, too barbaric to run in reality. Imagine letting a group of a few dozen humans grow up without any contact with language and the modern world. Are you confident they would develop language? I'm not sure, personally.
I am entirely certain that those humans brought up with no contact with language would figure out language for themselves. Consider, for example, deaf children who were raised in the time before sign language was common. Those children consistently found a way to communicate. It may not be exactly like the language we use or be as complex — but it is language.
It's worth adding that there are two definitions of grammar which can result in misunderstanding and crossed wires. There's the prescriptive definition, more familiar to laypeople, which is "rules" like 'no split infinitives' and 'don't start a sentence with and' and so on. These were largely developed to constrain language. The other definition of grammar is moreso the intrinsic rules natural languages follows, ie syntax. I work on the latter and we would call it a fundamental part of language (language = alphabet + grammar) - it's basically patterns which form language that we can't easily explain, but we know that 'teapot nineteen boy the bounced several' doesn't follow them, and nor does 'threw stairs down a teapot did John', even though we can infer an intended meaning. (This is where the idea of universal grammar comes from, but they're not the same thing).
As an aside, thiis kind of grammar can apply to what people wouldn't consider languages; eg animals aren't considered to have language, but communications like bee dances and bird calls have been found to follow some underlying 'grammar'
As for the thought experiment, the closest I can think of is case studies of feral children and the like (caveat: highly criticised for reliability for various reasons). There is also some work on when human ancestors first developed language and which cognitive/behavioural developments it coincided with; to my recollection it was related to more complex organising of group members (eg you do x, then I'll do y, and later we do z with so-and-so) and also I think there are strong links to imagination and storytelling (pinch of salt, though, my memory is foggy on this)