I’m to allow user to draw his custom area on frontend (flutter) and pass it to backend (django +postgis) which must return list of PointFields thats are lies inside the curve. So, in which format should I pass the curve to the backen and how do I properly filter the places queryset?

Assuming you've got a model defined as
class Place(models.Model):
location = PointField()
You should be able to use the within lookup to retrieve all places with a location contained in the user provided geometry
Place.objects.filter(location__within=geometry)
I suggest you export the user selection as GeoJSON from the frontend and POST it to the backend. On the Django side you should be able to create a GEOSGeometry from the provided data
geometry = GEOSGeometry(request.POST['selection'])
Place.objects.filter(location__within=geometry)
You'll want to validate the selection is valid GeoJSON but this should at least get you started.
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