Thank you for keeping the conversation going, Carla! The questions you brought up are indeed very interesting. I can't help but think about writing a more detailed answer as soon as I get the time :D
My short-ish opinion is that:
Yes, language and wordplay are huge for brain development.
Being silly and deliberately modifying words as I talk to my son? It is not something I prefer doing because I'd rather teach him to speak his native language correctly (as much as I know it) instead of trying to spend time later on to correct him.
Here's one distinction that seems very important to me:
Silly talk initiated by the toddler VS silly talk initiated by the adult.
I respond to my child's invitations to play with language! I also make sure it's clear that we're playing when I do that.
He talks pretty well for his age. And he recently started to babble unintelligible words, pretending to speak in a foreign language. He'll say something like "Alksaj sidlar kas iewld" and then translate to me: "I want to drink water, that's what I said". If he does so, I serve him water. If he's babbling longer (he sometimes does so for up to a minute or more), I join the conversation and talk to him on his language, playing with the intonation to make it look like I ask questions or make exclamations.
Besides that, I have a couple of other strategies to play with words. Some of them are inspired by the particularities of our native language, Romanian.
He's asking me to formulate and change questions based on the subject of a sentence. He plays with a ball and puts it next to him, saying he's "holding it loved". I say, "I see that's your beloved ball," and he's asking how do I say if it's a book? Or if it's a dog? Or.... (depending on the noun gender, the "beloved" will take different forms in Romanian, as part of the agreement process)
We pick colors and name as many words as possible that we can associate with that color.
We talk about comparison degrees and use diminutives and augmentatives.
I sometimes talk to him in verses and point out the rhymes - "See what rhyme I found here?"
"Deconstructing and playing with language allowed us to explore it in new ways also to learn when and where which terms were appropriate." like you described, is something we do too, at the child's initiative.
I pay attention to the cues and encourage him to play with words as he feels.
But when he talks to me and makes a mistake - like using the wrong plural or the wrong genitive - I repeat what he said, replacing the wrong word with the correct form. I try to model proper speaking without emphasizing it and without saying "that's wrong".
This brings us to your idea that "language being 'correct' is an interesting topic".
It is, and I realize the term is somewhat relative.
But I'm confident we can all agree on some general standards, and parents certainly don't need to take "grammar" classes to teach their children to talk correctly. They have better things to do with their time. Still, when they know a word is incorrect or inappropriate, I think it is beneficial to help the child understand it too.
For instance, I'm all for colloquial language, but not so much for elements of slang and jargon.
I'm sure the child will bump into those eventually, and I'll be there to explain it to him when the time comes. Yet, I don't find it necessary to instruct him on too many slang words for now.
At least, this is my idea on talking to children correctly and respectfully at home. :D
Thank you for allowing me to think of all these in more detail!
Have an awesome week start,