2. It's a military invasion. The precedent of Operation Olive Branch indicates that calling this an "effort to stabilize" is an abuse of semantics.
3. Do you have any source indicating that Kurdish control is contributing to the displacement of people?
4. More about "efforts to stabilize": "Criticism of Turkish alleged support for Jihadists, including ISIL, and of targeting Kurds" https://en.wikipedia.org/wiki/Turkish_involvement_in_the_Syr...
Then what was America doing there?
It starts with an O and rhymes with way some old timey new yorkers say "girl"
Are you aware that this is wholly down to a deal between the EU and Turkey which includes, amongst others, payments of about 6bn EUR to Turkey?
[1] https://www.theguardian.com/cities/2019/jun/19/gaziantep-tur...
EU politicians were too afraid of the xenophobic shitstorm on the one hand, and the media catastrophe of thousands of boat-people drowning at sea.
So they complied. You never comply to a blackmail, there's no end to the demands.
It's not trying to do that, though that's the pretext. As with Turkey’s previous interventions in Syria and Iraq (and its ongoing internal campaigns), it's trying suppress the Kurds. If it's trying to create a pacified area, it's to avoid having a safe space for Kurds, not to repatriate Syrian refugees (except perhaps to repatriate non-Kurdish Syrian refugees to displace the Kurds, which is certainly a plausible Turkish strategic aim.)
And quite frankly, I don’t see any reason why Turkey would succeed. Just look how much trouble the (presumably better resourced and more experienced) US has had in setting up stable governments in Iraq and Afghanistan which (in my admittedly nonexpert opinion) seem to be the best historical parallels for attempting to create stable societies out of a legal vacuum with little-to-no useful institutions and peoples with minimal experience/exposure to operating in such a society.